JEE Physics

StemEZ

Chapter 6

Gravitation - all with Video Answers

Educators

Chapter Questions

Problem 668

Two identical solid copper spheres of radius $R$ are placed in contact with each other. The gravitational force between them is proportional to
(A) $\mathrm{R}^{2}$
(B) $\mathrm{R}^{-2}$
(C) $\mathrm{R}^{-4}$
(D) $\mathrm{R}^{4}$

Narendra Kumar

Narendra Kumar

Numerade Educator

Problem 669

The gravitational force Fg between two objects does not depend on
(A) sum of the masses
(B) product of masses
(C) Gravitational constant
(D) Distance between the masses

Brjesh Kumar

Numerade Educator

Problem 670

The atmosphere is held to the earth by
(A) clouds
(B) Gravity
(C) Winds
(D) None of the above

Narendra Kumar

Numerade Educator

Problem 671

Two sphere of mass $\mathrm{m}_{1}$ and $\mathrm{m}_{2}$ are situated in air and the gravitational force between them is $F$. The space around the masses is now filled with liquid of specific gravity 3 . The gravitational force will now be
(A) $\mathrm{F}$
(B) $3 \mathrm{~F}$
(C) $\mathrm{F} / 3$
(D) $\mathrm{F} / 9$.

Narendra Kumar

Numerade Educator

Problem 672

A satellite of the earth is revolving in a circular orbit with a uniform speed $\mathrm{v} .$ If the gravitational force suddenly disappears, the satellite will
(A) Continue to move with velocity $\mathrm{v}$ along the original orbit.
(B) Move with a Velocity $\mathrm{v}$, tangentially to the original orbit.
(C) Fall down with increasing velocity.
(D) Ultimately come to rest somewhere on the original orbit.

Narendra Kumar

Numerade Educator

Problem 673

Correct form of gravitational law is
(A) $\mathrm{F}=-\left[\left(\mathrm{Gm}_{1} \mathrm{~m}_{2}\right) / \mathrm{r}^{2}\right]$
(B) $\mathrm{F}^{-}=-\left[\left(\mathrm{Gm}_{1} \mathrm{~m}_{2}\right) / \mathrm{r}^{2}\right]$
(C) $\mathrm{F}^{-}=-\left[\left(\mathrm{Gm}_{1} \mathrm{~m}_{2}\right) / \mathrm{r}^{2}\right] \hat{\mathrm{r}}$
(B) $\mathrm{F}^{\rightarrow}=-\left[\left(\mathrm{Gm}_{1} \mathrm{~m}_{2}\right) / \mathrm{r}^{3}\right] \mathrm{r}^{-}$

Narendra Kumar

Numerade Educator

Problem 674

Mass $M$ is divided into two parts $\mathrm{xM}$ and $(1-\mathrm{x}) \mathrm{M}$. For a given separation, the value of $\mathrm{x}$ for which the gravitational force between the two pieces becomes maximum is
(A) 1
(B) 2
(C) $1 / 2$
(D) $4 / 5$

Narendra Kumar

Numerade Educator

Problem 675

The earth (mass $=6 \times 10^{24} \mathrm{~kg}$ ) revolves around the sun with angular velocity $2 \times 10^{-7} \mathrm{rad} / \mathrm{sec}$ in a circular orbit of radius $1.5 \times 10^{8} \mathrm{~km} .$ The force exerted by the sun on the earth is $=\ldots \ldots \ldots \ldots . \mathrm{N}$
(A) $18 \times 10^{25}$
(b) zero
(C) $27 \times 10^{39}$
(D) $36 \times 10^{21}$

Narendra Kumar

Numerade Educator

Problem 676

Two particle of equal mass go round a circle of radius $\mathrm{r}$. Under the action of their mutual gravitational force. The speed of each particle is $=\ldots \ldots \ldots \ldots \ldots$
(A) $\mathrm{U}=(1 / 2 \mathrm{r}) \sqrt{(1} / \mathrm{Gm})$
(B) $\mathrm{U}=\sqrt{(\mathrm{Gm} / 2 \mathrm{r})}$
(C) $\mathrm{U}=(1 / 2) \sqrt{(\mathrm{Gm} / \mathrm{r})}$
(D) $\mathrm{U}=\sqrt{[}(4 \mathrm{Gm}) / \mathrm{r}]$

Narendra Kumar

Numerade Educator

Problem 677

The distance of the moon and earth is $D$ the mass of earth is 81 times the mass of moon. At what distance from the center of the earth, the gravitational force will be zero
(A) $\mathrm{D} / 2$
(B) $[(12 \mathrm{D}) / 3]$
(C) $(4 \mathrm{D} / 3)$
(D) $(9 \mathrm{D} / 10)$

Narendra Kumar

Numerade Educator

Problem 678

One can easily find "Weight of the earth" by calculating the mass of earth using the formula (in usual notation)
(A) $(\mathrm{g} / \mathrm{G}) \mathrm{Re}$
(B) $(\mathrm{g} / \mathrm{G}) \mathrm{Re}^{2}$
(C) $(\mathrm{G} / \mathrm{g}) \mathrm{Re}^{2}$
(D) $(\mathrm{G} / \mathrm{g}) \mathrm{Re}^{3}$

Narendra Kumar

Numerade Educator

Problem 679

Three equal masses of $\mathrm{m} \mathrm{kg}$ each are placed at the vertices of an equilateral triangle $\mathrm{PQR}$ and a mass of $2 \mathrm{~m} \mathrm{~kg}$ is placed at the centroid 0 of the triangle which is at a distance of $\sqrt{2} \mathrm{~m}$ from each of vertices of triangle. The force in newton acting on the mass $2 \mathrm{~m}$ is $=\ldots \ldots \ldots$..
(A) 2
(B) 1
(C) $\sqrt{2}$
(D) zero

Narendra Kumar

Numerade Educator

Problem 680

Which of the following statement about the gravitational constant is true
(A) It is a force
(B) It has no unit
(C) It has same value in all system of unit
(D) It depends on the value of the masses.

Brjesh Kumar

Numerade Educator

Problem 681

Two point masses $\mathrm{A}$ and $\mathrm{B}$ having masses in the ratio $4: 3$ are separated by a distance of $\operatorname{lm}$. When another point mass of mass $\mathrm{M}$ is placed in between $\mathrm{A}$ and $\mathrm{B}$ the forces $\mathrm{A}$ and is $(1 / 3 \mathrm{rd})$ of the force between $\mathrm{B}$ and $\mathrm{C}$, Then the distance $\mathrm{C}$ from $\mathrm{A}$ is $=\ldots \ldots \ldots \mathrm{m}$
(A) $(2 / 3)$
(B) $1 / 3$
(C) $1 / 4$
(D) $2 / 7$

Narendra Kumar

Numerade Educator

Problem 682

The gravitational force between two point masses $\mathrm{m}_{1}$ and $\mathrm{m}_{2}$ and separation $\mathrm{r}$ is given by $\mathrm{F}=\mathrm{G}\left[\left(\mathrm{m}_{1} \mathrm{~m}_{2}\right) / \mathrm{r}^{2}\right]$ The constant $K \ldots \ldots$
(A) Depends on system of units only.
(B) Depends on medium between masses only.
(C) Depends on both (a) and (b)
(D) is independent of both (a) and (b)

Narendra Kumar

Numerade Educator

Problem 683

As we go from the equator to the poles, the value of $g \ldots \ldots \ldots$
(A) Remains constant
(B) Decreases
(C) Increases
(D) Decreases upto latitude of $45^{\circ}$

Aja S

Numerade Educator

Problem 684

If $R$ is the radius of the earth and $g$ the acceleration due to gravity on the earth's surface, the mean density of the earth is $=\ldots \ldots \ldots$
(A) $[(4 \pi \mathrm{G}) /(3 \mathrm{~g} \mathrm{R})]$
(B) $[(3 \pi R) /(4 \mathrm{gG})]$
(C) $[(3 \mathrm{~g}) /(4 \pi \mathrm{RG})]$
(D) $[(\pi R G) /(12 g)]$

Narendra Kumar

Numerade Educator

Problem 685

The radius of the earth is $6400 \mathrm{~km}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2} .$ In order that a body of $5 \mathrm{~kg}$ weights zero at the equator, the angular speed of the earth is $=\ldots \ldots \ldots \mathrm{rad} / \mathrm{sec}$
(A) $(1 / 80)$
(B) $[1 /(400)]$
(C) $[1 /(800)]$
(D) $[1 /(600)]$

Narendra Kumar

Numerade Educator

Problem 686

The time period of a simple pendulum on a freely moving artificial satellite is .......... sec
(A) 0
(B) 2
(C) 3
(D) Infinite

Narendra Kumar

Numerade Educator

Problem 687

A spherical planet far out in space has mass $\mathrm{M}_{0}$ and diameter $\mathrm{D}_{0}$. A particle of $\mathrm{m}$ falling near the surface of this planet will experience an acceleration due to gravity which is equal to
(A) $\left[\left(\mathrm{GM}_{0}\right) /\left(\mathrm{D}_{\circ}^{2}\right)\right]$
(B) $\left[\left(4 \mathrm{mGM}_{0}\right) /\left(\mathrm{D}_{0}^{2}\right)\right]$
(C) $\left[\left(4 \mathrm{GM}_{0}\right) /\left(\mathrm{D}_{0}^{2}\right)\right]$
(D) $\left[\left(\mathrm{GmM}_{0}\right) /\left(\mathrm{D}_{\circ}^{2}\right)\right]$

Narendra Kumar

Numerade Educator

Problem 688

A body weights $700 \mathrm{~g} \mathrm{wt}$ on the surface of earth. How much it weight on the surface of planet whose mass is $1 / 7$ and radius is half that of the earth
(A) $200 \mathrm{~g} \mathrm{wt}$
(B) $400 \mathrm{~g} \mathrm{wt}$
(C) $50 \mathrm{~g} \mathrm{wt}$
(D) $300 \mathrm{~g}$ wt.

Narendra Kumar

Numerade Educator

Problem 689

The value of $g$ on the earth surface is $980 \mathrm{~cm} / \mathrm{sec}^{2}$. Its value at a height of $64 \mathrm{~km}$ from the earth surface is $\ldots \ldots . \mathrm{cms}^{-2}$
(A) $960.40$
(B) $984.90$
(C) $982.45$
(D) $977.55$

Narendra Kumar

Numerade Educator

Problem 690

If earth rotates faster than its present speed the weight of an object will.
(A) increases at the equator but remain unchanged of the poles.
(B) Decreases at the equator but remain unchanged at poles.
(C) Remain unchanged at the equator but decreases at poles.
(D) Remain unchanged at the equator but increases at the poles.

Narendra Kumar

Numerade Educator

Problem 691

The moon's radius is $1 / 4$ that of earth and its mass is $1 / 80$ times that of the earth. If g represents the acceleration due to gravity on the surface of earth, that on the surface of the moon is
(A) $g / 4$
(B) $\mathrm{g} / 5$
(c) $\mathrm{g} / 6$
(D) $\mathrm{g} / 8$

Narendra Kumar

Numerade Educator

Problem 692

The depth of at which the value of acceleration due to gravity becomes $1 / \mathrm{n}$ the time the value of at the surface is $(\mathrm{R}=$ radius of earth $)$
(A) $\mathrm{R} / \mathrm{n}$
(B) $R[(\mathrm{n}-1) / \mathrm{n}]$
(C) $\left(\mathrm{R} / \mathrm{n}^{2}\right)$
(D) $\mathrm{R}[\mathrm{n} /(\mathrm{n}+1)]$

Narendra Kumar

Numerade Educator

Problem 693

If the density of small planet is that of the same as that of the earth while the radius of the planet is $0.2$ times that of the earth, the gravitational acceleration on the surface of the planet is
(A) $0.2 \mathrm{~g}$
(B) $0.4 \mathrm{~g}$
(C) $2 \mathrm{~g}$
(D) $4 \mathrm{~g}$

Narendra Kumar

Numerade Educator

Problem 694

If mass of a body is $\mathrm{M}$ on the earth surface, than the mass of the same body on the moon surface is
(A) $\mathrm{M} / 6$
(B) 56
(C) $\mathrm{M}$
(D) None of these

Narendra Kumar

Numerade Educator

Problem 695

An object weights $72 \mathrm{~N}$ on the earth. Its weight at a height $(\mathrm{R} / 2)$ from earth is $=\ldots \ldots \ldots \ldots \ldots \mathrm{N}$
(A) 32
(B) 56
(C) 72
(D) zero

Narendra Kumar

Numerade Educator

Problem 696

If the radius of earth is $\mathrm{R}$ then height ${ }^{\prime} \mathrm{h}$ ' at which value of ' $\mathrm{g}$ ' becomes one-fourth is
(A) $\mathrm{R} / 4$
(B) $3 \mathrm{R} / 4$
(C) $\mathrm{R}$
(D) $\mathrm{R} / 8$

Narendra Kumar

Numerade Educator

Problem 697

If the mass of earth is 80 times of that of a planet and diameter is double that of planet and ' $\mathrm{g}$ ' on the earth is $9.8 \mathrm{~ms}^{-2}$, then the value of $\mathrm{g}^{\prime}$ on that planet is $=\ldots \ldots \ldots \mathrm{ms}^{-2}$
(A) $4.9$
(B) $0.98$
(C) $0.49$
(D) 49

Narendra Kumar

Numerade Educator

Problem 698

Assuming earth to be a sphere of a uniform density, what is value of gravitational acceleration in mine $100 \mathrm{~km}$ below the earth surface $=\ldots \ldots \ldots \ldots \mathrm{ms}^{-2}$
(A) $9.66$
(B) $7.64$
(C) $5.00$
(D) $3.1$

Narendra Kumar

Numerade Educator

Problem 699

Let $g$ be the acceleration due to gravity at earth's surface and $\mathrm{k}$ be the rotational $\mathrm{K} . \mathrm{E}$. of earth suppose the earth's radius decreases by $2 \%$ keeping alt other quantities same then
(A) $g$ decreases by $2 \%$ and $\mathrm{K}$ decreases by $4 \%$
(B) $g$ decreases by $4 \%$ and $K$ increases by $2 \%$
(C) $\mathrm{g}$ increases by $4 \%$ and $\mathrm{K}$ increases by $4 \%$
(D) g decreases by $4 \%$ and $\mathrm{K}$ increases by $4 \%$

Narendra Kumar

Numerade Educator

Problem 700

A body weight $500 \mathrm{~N}$ on the surface of the earth. How much would it weight half way below the surface of earth
(A) $125 \mathrm{~N}$
(B) $250 \mathrm{~N}$
(C) $500 \mathrm{~N}$
(D) $1000 \mathrm{~N}$

Narendra Kumar

Numerade Educator

Problem 701

The radii of two planets are respectively $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ and their densities are respectively $\rho_{1}$ and $\rho_{2}$ the ratio of the accelerations due to gravity at their surface is
(A) $g_{1}: g_{2}=\left(\rho_{1} / R_{1}^{2}\right) \cdot\left(\rho_{2} / R_{2}^{2}\right)$
(B) $\mathrm{g}_{1}: \mathrm{g}_{2}=\mathrm{R}_{1} \mathrm{R}_{2}: \rho_{1} \rho_{2}$
(C) $g_{1}: g_{2}=R_{1} \rho_{2} \cdot R_{2} p_{1}$
(D) $g_{1}: g_{2}=R_{1} \rho_{1}: R_{2} \rho_{2}$

Narendra Kumar

Numerade Educator

Problem 702

At what height over the earth's pole, the free fall acceleration decreases by one percent $=\ldots \ldots \ldots \mathrm{km}(\mathrm{Re}=6400 \mathrm{~km})$
(A) 32
(B) 80
(C) $1.253$
(D) 64

Narendra Kumar

Numerade Educator

Problem 703

Weight of a body is maximum at
(A) moon
(B) poles of earth
(C) Equator of earth
(D) Center of earth

Narendra Kumar

Numerade Educator

Problem 704

At what distance from the center of earth, the value of acceleration due to gravity $g$ will be half that of the surfaces $(\mathrm{R}=$ Radius of earth $)$
(A) $2 \mathrm{R}$
(B) $\mathrm{R}$
(C) $1.414 \mathrm{R}$
(D) $0.414 \mathrm{R}$

Narendra Kumar

Numerade Educator

Problem 705

The acceleration due to gravity near the surface of a planet of radius $\mathrm{R}$ and density $\mathrm{d}$ is proportional to
(A) $\mathrm{d} / \mathrm{R}^{2}$
(B) $\mathrm{d} \mathrm{R}^{2}$
(C) $\mathrm{dR}$
(D) $\mathrm{d} / \mathrm{R}$

Narendra Kumar

Numerade Educator

Problem 706

The acceleration due to gravity is $g$ at a point distance $r$ from the center of earth $\mathrm{R}$. if $\mathrm{r}<\mathrm{R}$ then
(A) $g \propto r$
(B) $g \propto r^{2}$
(C) $g \propto \mathrm{r}^{-2}$
(D) $g \propto r^{-1}$

Narendra Kumar

Numerade Educator

Problem 707

The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of earth. If the radius of the earth is $\mathrm{R}$, the radius of planet would be
(A) $2 \mathrm{R}$
(B) $4 \mathrm{R}$
(C) $1 / 4 \mathrm{R}$
(D) $\mathrm{R} / 2$

Narendra Kumar

Numerade Educator

Problem 708

Density of the earth is doubled keeping its radius constant then acceleration, due to gravity will be $-m s^{-2}$
$\left(\mathrm{g}=9.8 \mathrm{~ms}^{2}\right)$
(A) $19.6$
(B) $9.8$
(C) $4.9$
(D) $2.45$

Narendra Kumar

Numerade Educator

Problem 709

Weight of body of mass $\mathrm{m}$ decreases by $1 \%$ when it is raised to height $\mathrm{h}$ above the earth's surface. If the body is taken to a depth $\mathrm{h}$ in a mine. change in its weight is
(A) $2 \%$ decreases
(B) $0.5 \%$ decreases
(C) $1 \%$ increases
(D) $0.5 \%$ increases

Narendra Kumar

Numerade Educator

Problem 710

If density of earth increased 4 times and its radius becomes half of then out weight will be...
(A) Four times it present value
(B) doubled
(C) Remain same
(D) halved

Narendra Kumar

Numerade Educator

Problem 711

A man can jump to a height of $1.5 \mathrm{~m}$ on a planet $\mathrm{A}$ what is the height ne may be able to jump on another planet whose density and radius are respectively one-quarter and one-third that of planet $\mathrm{A}$
(A) $1.5 \mathrm{~m}$
(B) $15 \mathrm{~m}$
(C) $18 \mathrm{~m}$
(D) $28 \mathrm{~m}$

Narendra Kumar

Numerade Educator

Problem 712

If the value of ' $\mathrm{g}$ ' acceleration due to gravity, at earth surface is $10 \mathrm{~ms}^{-2}$. its value in $\mathrm{ms}^{-2}$ at the center of earth, which is assumed to be a sphere of Radius ' $\mathrm{R}$ 'meter and uniform density is
(A) 5
(B) $10 / \mathrm{R}$
(C) $10 / 2 \mathrm{R}$
(D) zero

Narendra Kumar

Numerade Educator

Problem 713

A research satellite of mass $200 \mathrm{~kg}$. Circles the earth in an orbit of average radius $(3 \mathrm{R} / 2)$ where $\mathrm{R}$ is radius of earth. Assuming the gravitational pull $10 \mathrm{~N}$, the pull on the satellite will be $=\mathrm{N}$
(A) 880
(B) 889
(C) 890
(D) 892

Narendra Kumar

Numerade Educator

Problem 714

- Acceleration due to gravity on moon is $1 / 6$ of the acceleration due to gravity on earth. If the ratio of densities of earth $\rho_{\mathrm{e}}$ and moon $\rho_{\mathrm{m}}$ is $\left(\rho_{\mathrm{e}} / \rho_{\mathrm{m}}\right)=5 / 3$ then radius of moon $\mathrm{R}_{\mathrm{e}}$ in terms of $\mathrm{R}_{\mathrm{e}}$ will be
(A) $(5 / 18) \mathrm{R}_{\mathrm{e}}$
(B) $(1 / 6) \mathrm{R}_{\mathrm{e}}$
(C) $(3 / 16) \mathrm{R}_{\mathrm{e}}$
(D) $[1 /(2 \sqrt{3})] R_{e}$

Narendra Kumar

Numerade Educator

Problem 715

The acceleration of a body due to the attraction of the earth (radius R) at a distance $2 \mathrm{R}$ from the surface of the earth is $=$ (g $=\overline{\text { acceleration due to gravity at the surface of earth })}$
(A) $\mathrm{g} / 9$
(B) $\mathrm{g} / 3$
(C) $\mathrm{g} / 4$
(D) 9

Narendra Kumar

Numerade Educator

Problem 716

The height at which the weight of a body becomes $1 / 16$ th its weight on the surface of (radius $\mathrm{R}$ ) is
(A) $3 \mathrm{R}$
(B) $4 \mathrm{R}$
(C) $5 \mathrm{R}$
(D) $15 \mathrm{R}$

Narendra Kumar

Numerade Educator

Problem 717

A spherical planet has a mass $\mathrm{M}_{\mathrm{P}}$ and diameter $\mathrm{D}_{\mathrm{P}} \mathrm{A}$ particle of mass $\mathrm{m}$ falling freely near the surface of this planet will experience an acceleration due to gravity, equal to
(A) $\left[\left(4 \mathrm{GM}_{\mathrm{P}}\right) /\left(\mathrm{D}_{\mathrm{P}}^{2}\right)\right]$
(B) $\left[\left(\mathrm{GM}_{\mathrm{P}} \mathrm{m}\right) /\left(\mathrm{D}_{\mathrm{P}}^{2}\right)\right]$
(C) $\left[\left(\mathrm{GM}_{\mathrm{P}}\right) /\left(\mathrm{D}_{\mathrm{P}}^{2}\right)\right]$
(D) $\left[\left(4 \mathrm{GM}_{\mathrm{P}} \mathrm{m}\right) /\left(\mathrm{D}_{\mathrm{P}}^{2}\right)\right]$

Narendra Kumar

Numerade Educator

Problem 718

Assuming the earth to have a constant density, point out which of following curves show the variation acceleration due to gravity from center of earth to points far away from the surface of earth $\ldots \ldots \ldots \ldots$

Narendra Kumar

Numerade Educator

Problem 719

In a gravitational field, at a point where the gravitational potential is zero
(A) The gravitational field is necessarily zero
(B) The gravitational field is not necessarily zero
(C) Nothing can be said definitely, about the gravitational field
(D) None of these

Aja S

Numerade Educator

Problem 720

The mass of the earth is $6.00 \times 10^{24} \mathrm{~kg}$ and that of the moon is $7.40 \times 10^{22} \mathrm{~kg}$. The constant of gravitation $\mathrm{G}=6.67 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{~kg}^{-2}$. The potential energy of the
system is $-7.79 \times 10^{28}$ joules the mean distance between the earth and moon is $=$ meter.
(A) $3.80 \times 10^{8}$
(B) $3.37 \times 10^{8}$
(C) $7.60 \times 10^{8}$
(D) $1.90 \times 10^{2}$

Narendra Kumar

Numerade Educator

Problem 721

The masses and radii of earth and moon are $M_{1}, R_{1}$ and $\mathrm{M}_{2}, \mathrm{R}_{2}$ respectively. Their centers are d distance of apart. The minimum velocity with which a particle of mass $\mathrm{m}$ should be projected from a point midway between their centers so that it escapes to infinity is
(B) $\left.2 \sqrt{[}(2 \mathrm{G} / \mathrm{d})\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)\right]$
(D) $2 \sqrt{\left[\left\{\mathrm{Gm}\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)\right\} /\left\{\mathrm{d}\left(\mathrm{R}_{1}+\mathrm{R}_{2}\right)\right\}\right]}$

Subash Charan

Numerade Educator

Problem 722

A rocket is launched with velocity $10 \mathrm{kms}^{-1}$. If radius of earth is $R$ then maximum height attained by it will be =
(A) $2 \mathrm{R}$
(B) $3 \mathrm{R}$
(C) $4 \mathrm{R}$
(D) $5 \mathrm{R}$

Narendra Kumar

Numerade Educator

Problem 723

What is the intensity of gravitational field at the center of spherical shell
(A) $\left(\mathrm{Gm} / \mathrm{r}^{2}\right)$
(B) $\mathrm{g}$
(C) zero
(D) None of these

Narendra Kumar

Numerade Educator

Problem 724

Escape velocity of a body of $1 \mathrm{~kg}$ on a planet is $100 \mathrm{~ms}^{-1}$. Gravitational potential energy of the body at the planet is $=$
$\begin{array}{ll}\text { (A) } \overline{-5000} & \text { (B) }-1000\end{array}$
(C) $-2400$
(D) 5000

Narendra Kumar

Numerade Educator

Problem 725

A body of mass $\mathrm{m} \mathrm{kg}$ starts falling from a point $2 \mathrm{R}$ above the earth's surface. Its $\mathrm{K} . \mathrm{E}$. when it has fallen to a point ' $\mathrm{R}$ ' above the Earth's surface $=\ldots \ldots \ldots \ldots J$ [R - Radius of Earth, M-mass of Earth G-Gravitational constant $]$
(A) $(1 / 2)[(\mathrm{GMm}) / \mathrm{R}]$
(B) $(1 / 6)[(\mathrm{GMm}) / \mathrm{R}]$
(C) $(2 / 3)[(\mathrm{GMm}) / \mathrm{R}]$
(D) $(1 / 3)[(\mathrm{GMm}) / \mathrm{R}]$

Narendra Kumar

Numerade Educator

Problem 726

The Gravitational P.E. of a body of mass $\mathrm{m}$ at the earth's surface is $-\mathrm{mgRe}$. Its gravitational potential energy at a height $\operatorname{Re}$ from the earth's surface will be $=\ldots \ldots \ldots$ here (Re is the radius of the earth)
(A) $-2 \mathrm{mgRe}$
(B) $2 \mathrm{mgRe}$
(C) $(1 / 2) \mathrm{mg} \mathrm{Re}$
(D) $-(1 / 2) \mathrm{mg} \operatorname{Re}$

Narendra Kumar

Numerade Educator

Problem 727

A body is projected vertically upwards from the surtace of a planet of radius $\mathrm{R}$ with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is $\ldots \ldots \ldots \ldots$
(A) $(\mathrm{R} / 3)$
(B) $(\mathrm{R} / 2)$
(C) $(\mathrm{R} / 4)$
(D) $(\mathrm{R} / 5)$

Narendra Kumar

Numerade Educator

Problem 728

Energy required to move a body of mass $\mathrm{m}$ from from an orbit of radius $2 \mathrm{R}$ to $3 \mathrm{R}$ is $\ldots \ldots \ldots \ldots$
(A) $\left[(\mathrm{GMm}) /\left(12 \mathrm{R}^{2}\right)\right]$
(B) $\left[(\mathrm{GMm}) /\left(3 \mathrm{R}^{2}\right)\right]$
(C) $[(\mathrm{GMm}) /(8 \mathrm{R})]$
(D) $[(\mathrm{GMm}) /(6 \mathrm{R})]$

Narendra Kumar

Numerade Educator

Problem 729

Radius of orbit of satellite of earth is $\mathrm{R}$. Its $\mathrm{KE}$ is proportional to
(A) $(1 / R)$
(B) $(1 / \sqrt{\mathrm{R}})$
(C) $\mathrm{R}$
(D) $\left(1 / \mathrm{R}^{3 / 2}\right)$

Narendra Kumar

Numerade Educator

Problem 730

A particle falls towards earth from infinity. It's velocity reaching the earth would be $\ldots \ldots \ldots$
(A) infinity
(B) $\sqrt{(2 g R)}$
(C) $2 \sqrt{(g R)}$
(D) zero

Narendra Kumar

Numerade Educator

Problem 731

The escape velocity for a sphere of mass $\mathrm{m}$ from earth having mass $\mathrm{M}$ and Radius $\mathrm{R}$ mass is given by
(A) $\sqrt{[}(2 \mathrm{GM}) / \mathrm{R}]$
(B) $2 \sqrt{(\mathrm{GM} / \mathrm{R})}$
(C) $\sqrt{[}(2 \mathrm{GMm}) / \mathrm{R}]$
(D) $\sqrt{(\mathrm{GM} / \mathrm{R})}$

Narendra Kumar

Numerade Educator

Problem 732

The escape velocity for a rocket from earth is $11.2 \mathrm{kms}^{-1}$ value on a planet where acceleration due to gravity is double that on earth and diameter of the planet is twice that of earth will be $=\ldots \ldots \ldots \ldots \mathrm{kms}^{-1}$
(A) $11.2$
(B) $22.4$
(C) $5.6$
(C) $53.6$

Ajay Singhal

Numerade Educator

Problem 733

The escape velocity from the earth is about $11 \mathrm{kms}^{-1}$. The escape velocity from a planet having twice the radius and the same mean density as the earth is $=\ldots \ldots \ldots \ldots \mathrm{kms}^{-1}$.
(A) 22
(B) 11
(C) $5.5$
(D) $15.5$

Subash Charan

Numerade Educator

Problem 734

If $\mathrm{g}$ is the acceleration due to gravity at the earth's surface and $\mathrm{r}$ is the radius of the earth, the escape velocity for the body to escape out of earth's gravitational field is $\ldots \ldots \ldots$
(A) $\mathrm{gr}$
(B) $\sqrt{(2 \mathrm{gr})}$
(C) $\mathrm{g} / \mathrm{r}$
(D) $\mathrm{r} / \mathrm{g}$

Ajay Singhal

Numerade Educator

Problem 735

The escape velocity of a projectile from the earth is approximately
(A) $11.2 \mathrm{kms}^{-1}$
(B) $112 \mathrm{kms}^{-1}$
(C) $11.2 \mathrm{~ms}^{-1}$
(D) $1120 \mathrm{kms}^{-1}$

Subash Charan

Numerade Educator

Problem 736

The escape velocity of a particle of mass $\mathrm{m}$ varies as........
(A) $\mathrm{m}^{2}$
(B) $\mathrm{m}$
(C) $\mathrm{m}^{0}$
(D) $\mathrm{m}^{-1}$

Narayan Hari

Numerade Educator

Problem 737

The escape velocity of an object from the earth depends upon the mass of earth (M), its mean density ( $p$ ), its radius
(R) and gravitational constant (G), thus the formula for escape velocity is
(A) $U=\mathrm{R} \sqrt{[}(8 \pi / 3) \mathrm{Gp}]$
(C) $\mathrm{U}=\sqrt{(2 \mathrm{GMR})}$
(D) $U=\sqrt{\left[(2 \mathrm{GMR}) / \mathrm{R}^{2}\right]}$

Saman Zulfiqar

Numerade Educator

Problem 738

Two small and heavy sphere, each of mass $\mathrm{M}$, are placed distance r apart on a horizontal surface the gravitational potential at a mid point on the line joining the center of spheres is
(A) zero
(B) $-(\mathrm{GM} / \mathrm{r})$
(C) $-[(2 \mathrm{GM}) / \mathrm{r}]$
(D) $-[(4 \mathrm{GM}) / \mathrm{r}]$

Saman Zulfiqar

Numerade Educator

Problem 739

The escape velocity of a body from earth's surface is Ve. The escape velocity of the same body from a height equal to 7 R from earth's surface will be
(A) $(\mathrm{Ve} / \sqrt{2})$
(B) $(\mathrm{Ve} / 2)$
(C) $(\mathrm{Ve} / 2 \sqrt{2})$
(D) $(\mathrm{Ve} / 4)$

Saman Zulfiqar

Numerade Educator

Problem 740

An artificial satellite is revolving round the earth in a circular orbit. its velocity is half the escape velocity. Its height from the earth surface is $=\ldots \ldots \ldots \ldots \mathrm{km}$
(A) 6400
(B) 12800
(C) 3200
(D) 1600

Subash Charan

Numerade Educator

Problem 741

The escape velocity of a planet having mass 6 times and radius 2 times as that of earth is
(A) $\sqrt{3} \mathrm{~V}_{\mathrm{e}}$
(B) $3 \mathrm{~V}_{\mathrm{e}}$
(C) $\sqrt{2} \mathrm{~V}_{\mathrm{e}}$
(D) $2 \mathrm{~V}_{\mathrm{e}}$

Ajay Singhal

Numerade Educator

Problem 742

There are two planets, the ratio of radius of two planets is $\mathrm{k}$ but the acceleration due to gravity of both planets are $\mathrm{g}$ what will be the ratio of their escape velocity.
(A) $(\mathrm{kg})^{1 / 2}$
(B) $(\mathrm{kg})^{-1 / 2}$
(C) $(\mathrm{kg})^{2}$
(D) $(\mathrm{kg})^{-2}$

Narayan Hari

Numerade Educator

Problem 743

The escape velocity of a body on the surface of the earth is $11.2 \mathrm{~km} / \mathrm{sec}$. If the mass of the earth is increases to twice its present value and the radius of the earth becomes half, the escape velocity becomes $=\ldots \ldots \ldots \ldots \mathrm{kms}^{-1}$
$(\Delta) 56$

Ajay Singhal

Numerade Educator

Problem 744

Given mass of the moon is $(1718)$ of the mass of the earth and corresponding radius is $(1 / 4)$ of the earth, If escape velocity on the earth surface is $11.2 \mathrm{kms}^{-1}$ the value of same on the surface of moon is $=\ldots \ldots \ldots \ldots \mathrm{kms}^{-1}$.
(A) $0.14$
(B) $0.5$
(C) $2.5$
(D) 5

Subash Charan

Numerade Educator

Problem 745

3 particle each of mass $\mathrm{m}$ are kept at vertices of an equilateral triangle of side $L$. The gravitational field at center due to these particles is
(A) zero
(B) $\left[(3 \mathrm{GM}) / \mathrm{L}^{2}\right]$
(C) $\left[(9 \mathrm{GM}) / \mathrm{L}^{2}\right]$
(D) $(12 / \sqrt{3})\left(\mathrm{Gm} / \mathrm{L}^{2}\right)$

Subash Charan

Numerade Educator

Problem 746

Escape velocity on the surface of earth is $11.2 \mathrm{kms}^{-1}$ Escape velocity from a planet whose masses the same as that of earth and radius $1 / 4$ that of earth is $=\ldots \ldots \ldots \mathrm{kms}^{-1}$
(A) $2.8$
(B) $15.6$
(C) $22.4$
(D) $44.8$

Ajay Singhal

Numerade Educator

Problem 747

The velocity with which a projectile must be fired so that it escapes earth's gravitational does not depend on $\ldots \ldots \ldots$
(A) mass of earth
(B) Mass of the projectile
(C) Radius of the projectiles' orbit
(D) Gravitational constant

Averell Hause

Carnegie Mellon University

Problem 748

The escape velocity for a body projected vertically upwards from the surface of earth is $11 \mathrm{kms}^{-1}$. If the body is projected at an angle of $45^{\circ}$ with the vertical, the escape velocity will be $\ldots \ldots \ldots \mathrm{kms}^{-1}$
(A) $(11 / \sqrt{2})$
(B) $11 \sqrt{2}$
(C) 22
(D) 11

Narayan Hari

Numerade Educator

Problem 749

The acceleration due to gravity on a planet is same as that on earth and its radius is four times that of earth. What will be the value of escape velocity on that planet if it is $\mathrm{V}_{\mathrm{e}}$ on the earth
(A) $\mathrm{V}_{\mathrm{e}}$
(B) $2 \mathrm{~V}_{\mathrm{e}}$
(C) $4 \mathrm{~V}_{\mathrm{e}}$
(D) $\mathrm{V}_{\mathrm{e}} / 2$

Supratim Pal

Numerade Educator

Problem 750

A particle of mass $10 \mathrm{~g}$ is kept on the surface of a uniform sphere of mass $100 \mathrm{~kg}$ and radius $10 \mathrm{~cm}$. Find the work to be done against the gravitational force between them to take the particle is away from the sphere $\left(\mathrm{G}=6.67 \times 10^{-11} \mathrm{SI}\right.$ unit $)$
(A) $6.67 \times 10^{-9} \mathrm{~J}$
(B) $6.67 \times 10^{-10} \mathrm{~J}$
(C) $13.34 \times 10^{-10} \mathrm{~J}$
(D) $3.33 \times 10^{-10} \mathrm{~J}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 751

A particle of mass $\mathrm{M}$ is situated at the center of a spherical shell of same mass and radius a the magnitude of gravitational potential at a point situated at (a/2) distance from the center will be
(A) $[(4 \mathrm{GM}) / \mathrm{a}]$
(B) $(\mathrm{GM} / \mathrm{a})$
(C) $[(2 \mathrm{GM}) / \mathrm{a}]$
(D) $[(3 \mathrm{GM}) / \mathrm{a}]$

Subash Charan

Numerade Educator

Problem 752

The mass and radius of the sun are $1.99 \times 10^{30} \mathrm{~kg}$ and $\mathrm{R}=6.96 \times 10^{8} \mathrm{~m}$. The escape velocity of rocket from the sun $\mathrm{is}=\ldots \ldots \ldots \mathrm{km} / \mathrm{sec}$
$\begin{array}{llll}\text { (A } 11.2 & \text { (B) } 12.38 & \text { (C) } 59.5 & \text { (D) } 618\end{array}$

Ravi Lall

Numerade Educator

Problem 753

The mass of a space ship is $1000 \mathrm{~kg} .$ It is to be launched from earth's surface out into free space the value of $\mathrm{g}$ and $\mathrm{R}$ (radius of earth) are $10 \mathrm{~ms}^{-2}$ and $6400 \mathrm{~km}$ respectively the required energy for this work will be $=\ldots \ldots \ldots .$ J
(A) $6.4 \times 10^{11}$
(B) $6.4 \times 10^{8}$
(C) $6.4 \times 10^{9}$
(D) $6.4 \times 10^{10}$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 754

The diagram showing the variation of gravitational potential of earth with distance from the centre of earth is

Hunza Gilgit

Numerade Educator

Problem 755

A sphere of mass $\mathrm{M}$ and Radius $\mathrm{R}_{2}$ has a concentric cavity of Radius $\mathrm{R}_{1}$ as shown in figure. The force $\mathrm{F}$ exerted by the sphere on a particle of mass $\mathrm{m}$ located at a distance $\mathrm{r}$ from the centre of sphere varies as $(\mathrm{O} \leq \mathrm{r} \leq \infty)$

Yuva S

Numerade Educator

Problem 756

Which one of the following graphs represents correctly the variation of the gravitational field with the distance (r) from the center of spherical shell of mass $\mathrm{M}$ and radius a

Subash Charan

Numerade Educator

Problem 757

which of the following graphs represents the motion of a planet moving about the sun.

Saman Zulfiqar

Numerade Educator

Problem 758

The curves for P.E. (U) K.E. (Ek) of two particle system as shown in figure. At what points system will be bound.
(A) Only at point D
(B) Only at point $\mathrm{A}$
(C) At point $\mathrm{D}$ and $\mathrm{A}$
(D) At points $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$

Sahil Patel

Numerade Educator

Problem 759

The correct graph representing the variation of total energy
(E) kinetic energy $(\mathrm{K})$ and potential energy $(\mathrm{U})$ of a satellite with its distance from the centre of earth is $\ldots \ldots$

Ajay Singhal

Numerade Educator

Problem 760

A shell of mass $\mathrm{M}$ and radius $\mathrm{R}$ has point mass $\mathrm{m}$ placed at a distance $r$ from its center. The gravitational potential energy $\mathrm{U}(\mathrm{r})-\mathrm{v}$ will be

Narayan Hari

Numerade Educator

Problem 761

If $\mathrm{V}_{\mathrm{e}}$ and $\mathrm{V}_{\mathrm{o}}$ are represent the escape velocity and orbital velocity of satellite corresponding to a circular orbit of
-adius $\mathrm{r}$, then
A) $\mathrm{V}_{\mathrm{e}}=\mathrm{V}_{\mathrm{o}}$
(B) $\sqrt{2} \mathrm{~V}_{\mathrm{o}}=\mathrm{V}_{\mathrm{e}}$
C) $\mathrm{V}_{\mathrm{e}}=\left(\mathrm{V}_{\mathrm{O}} / \sqrt{2}\right)$
(D) $\mathrm{V}_{\mathrm{e}}$ and $\mathrm{V}_{\mathrm{o}}$ are not related

Supratim Pal

Numerade Educator

Problem 762

If $\mathrm{r}$ represents the radius of the orbit of a satellite of mass m moving around a planet of mass $\mathrm{M}$, the velocity of the satellite is given by
(A) $\mathrm{U}^{2}=(\mathrm{gM} / \mathrm{r})$
(B) $\mathrm{U}^{2}=[(\mathrm{GMm}) / \mathrm{r}]$
(C) $\mathrm{U}=(\mathrm{GM} / \mathrm{r})$
(D) $\mathrm{U}^{2}=(\mathrm{GM} / \mathrm{r})$

Narayan Hari

Numerade Educator

Problem 763

Two satellites of mass $\mathrm{m}_{1}$ and $\mathrm{m}_{2}\left(\mathrm{~m}_{1}=\mathrm{m}_{2}\right)$ are revolving round the earth in circular orbits of $\mathrm{r}_{1}$ and $\mathrm{r}_{2}\left(\mathrm{r}_{1}>\mathrm{r}_{2}\right)$ respectively. Which of the following statement is true regarding their speeds $\mathrm{V}_{1}$ and $\mathrm{V}_{2}$
(A) $\mathrm{V}_{1}=\mathrm{V}_{2}$
(B) $\mathrm{V}_{1}<\mathrm{V}_{2}$
(C) $\mathrm{V}_{1}>\mathrm{V}_{2}$
(D) $\left(\mathrm{V}_{1} / \mathrm{r}_{1}\right)=\left(\mathrm{V}_{2} / \mathrm{r}_{2}\right)$

Hast Aggarwal

Numerade Educator

Problem 764

4 A satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the center of earth in new orbit is two times of the earlier orbit. The time period in second orbit is $\ldots \ldots \ldots \ldots$ hours.
(A) $4.8$
(B) $48 \sqrt{2}$
(C) 24
(D) $24 \sqrt{2}$

Supratim Pal

Numerade Educator

Problem 765

As astronaut orbiting the earth in a circular orbit $120 \mathrm{~km}$ above the surface of earth, gently drops a spoon out of space-ship. The spoon will
(A) Fall vertically down to the earth
(B) move towards the moon
(C) Will move along with space-ship
(D) Will move in an irregular wav then fall down to earth

Hast Aggarwal

Numerade Educator

Problem 766

The period of a satellite in circular orbit around a planet is independent of
(A) the mass of the planet
(B) the radius of the planet
(C) mass of the satellite
(D) all the three parameters (A), (B) and (C)

Narayan Hari

Numerade Educator

Problem 767

Two satellites $\mathrm{A}$ and $\mathrm{B}$ go round a planet $\mathrm{p}$ in circular orbits having radii $4 \mathrm{R}$ and $\mathrm{R}$ respectively if the speed of the satellite $\mathrm{A}$ is $3 \mathrm{~V}$, the speed if satellite $\mathrm{B}$ will be
(A) $12 \mathrm{~V}$
(B) $6 \mathrm{~V}$
(C) $4 / 3 \mathrm{~V}$
(D) $3 / 2 \mathrm{~V}$

Hast Aggarwal

Numerade Educator

Problem 768

A small satellite is revolving near earth's surface. Its orbital velocity will be nearly $=\ldots \ldots \ldots \ldots \mathrm{kms}^{-1}$.
(A) 8
(B) 4
(C) 6
(D) $11.2$

Hast Aggarwal

Numerade Educator

Problem 769

A satellite revolves around the earth in an elliptical orbit. Its speed
(A) is the same at all points in the orbit
(B) is greatest when it is closest to the earth
(C) is greatest when it is farthest to the earth
(D) goes on increasing or decreasing continuously depending upon the mass of the satellite

Zulfiqar Ali

Numerade Educator

Problem 770

If the height of a satellite from the earth is negligible in comparison of the radius of the earth $\mathrm{R}$, the orbital velocity of the satellite is
(A) $\mathrm{gR}$
(B) $(\mathrm{gR} / 2)$
(C) $\sqrt{(g} / \mathrm{R})$
(D) $\sqrt{(g R)}$

Narayan Hari

Numerade Educator

Problem 771

A satellite is moving around the earth with speed $\mathrm{v}$ in a circular orbit of radius $\mathrm{r}$. If the orbit radius is decreased by $1 \%$ its speed will
(A) increase by $1 \%$
(B) increase by $0.5 \%$
(C) decreased by $1 \%$
(C) Decreased by $0.5 \%$

Hast Aggarwal

Numerade Educator

Problem 772

orbital velocity of an artificial satellite does not depend upon
(A) mass of earth
(B) mass of satellite
(C) radius of earth
(D) acceleration due to gravity

James Kiss

Numerade Educator

Problem 773

orbital velocity of earth's satellite near the surface is $7 \mathrm{kms}^{-1}$. when the radius of orbit is 4 times that of earth's radius, then orbital velocity in that orbit is $=\ldots \ldots \ldots \ldots \mathrm{kms}^{-1}$
(A) $3.5$
(B) 17
(C) 14
(D) 35

Narendra Kumar

Numerade Educator

Problem 774

Two identical satellites are at $\mathrm{R}$ and $7 \mathrm{R}$ away from each surface, the wrong statement is ( $\mathrm{R}$ - Radius of earth)
(A) ratio of total energy will be 4
(B) ratio of kinetic energies will be 4
(C) ratio of potential energies will be 4
(D) ratio of total energy will be 4 but ratio of potential and kinetic energies will be 2

Yuva S

Numerade Educator

Problem 775

Which one of following statements regarding artificial satellite of earth is incorrect
(A) The orbital velocity depends on the mass of the satellite
(B) A minimum velocity of $8 \mathrm{kms}^{-1}$ is required by a satellite to orbit quite close to the earth.
(C) The period of revolution is large if the radius of its orbit is large
(D) The height of geostationary satellite is about $36000 \mathrm{~km}$ from earth

Subash Charan

Numerade Educator

Problem 776

The weight of an astronaut, in an artificial satellite revolving around the earth is
(A) zero
(B) Equal to that on the earth
(C) more than that on earth
(D) less than that on the earth

Hast Aggarwal

Numerade Educator

Problem 777

The distance of a geo-stationary satellite from the center of the earth (Radius $\mathrm{R}=6400 \mathrm{~km}$ ) is nearest to
(A) $5 \mathrm{R}$
(B) $7 \mathrm{R}$
(C) $10 \mathrm{R}$
(D) $18 \mathrm{R}$

Uma Kumari

Numerade Educator

Problem 778

A geo-stationary satellite is orbiting the earth of a height of $6 \mathrm{R}$ above the surface of earth, $\mathrm{R}$ being the radius of earth. The time period of another satellite at a height of $2.5 \mathrm{R}$ from the surface for earth is $=\ldots \ldots \ldots \ldots$
(A) 6
(B) $6 \sqrt{2}$
(C) 10
(D) $6 / \sqrt{2}$

Hast Aggarwal

Numerade Educator

Problem 779

If the gravitational force between two objects were proportional to $(1 / \mathrm{R})\left(\right.$ and not as $\left.1 / \mathrm{R}^{2}\right)$ where $\mathrm{R}$ is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to
(A) $\left(1 / \mathrm{R}^{2}\right)$
(B) $\mathrm{R}^{0}$
(C) $\mathrm{R}^{1}$
(D) $(1 / \mathrm{R})$

Hast Aggarwal

Numerade Educator

Problem 780

A satellite moves around the earth in a circular orbit of radius r with speed $v$, If mass of the satellite is $M$, its total energy is
(A) $-(1 / 2) \mathrm{MV}^{2}$
(B) $(1 / 2) \mathrm{MV}^{2}$
(C) $(3 / 2) \mathrm{MV}^{2}$
(D) $\mathrm{MV}^{2}$

Saman Zulfiqar

Numerade Educator

Problem 781

A satellite with K.E. $E_{\mathrm{k}}$ is revolving round the earth in a circular orbit. How much more K.E. should be given to it so that it may just escape into outer space ?
(A) $\mathrm{E}_{\mathrm{k}}$
(B) $2 \mathrm{E}_{\mathrm{k}}$
(C) $(1 / 2) \mathrm{E}_{\mathrm{k}}$
(D) $3 \mathrm{E}_{\mathrm{k}}$

Prabhu Ramji

Numerade Educator

Problem 782

Potential energy of a satellite having mass $\mathrm{m}$ and rotating at a height of $6.4 \times 10^{6} \mathrm{~m}$ from the surface of earth
(A) $-0.5 \mathrm{mg} \operatorname{Re}$
(B) $-\mathrm{mg} \mathrm{Re}$
(C) $-2 \mathrm{mgRe}$
(D) $4 \mathrm{mgRe}$

Hast Aggarwal

Numerade Educator

Problem 783

When a satellite going round the earth in a circular orbit of radius $\mathrm{r}$ and speed $\mathrm{v}$ loses some of its energy, then $\mathrm{r}$ and $\mathrm{v}$ changes as
(A) $r$ and $v$ both will increase
(B) $\mathrm{r}$ and $\mathrm{v}$ both will decease
(C) $r$ will decrease and $\mathrm{v}$ will increase
(D) $\mathrm{r}$ will increase and $\mathrm{v}$ will decrease

Andy Chen

Numerade Educator

Problem 784

The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to four times the previous value, the new time period will become $\ldots \ldots \ldots$ hours
(A) 10
(B) 120
(C) 40
(D) 80

Ajay Singhal

Numerade Educator

Problem 786

Two satellites $\mathrm{A}$ and $\mathrm{B}$ go round a planet in circular orbits having radii $4 \mathrm{R}$ and $\mathrm{R}$ respectively If the speed of satellite $\mathrm{A}$ is $3 \mathrm{v}$, then speed of satellite $\mathrm{B}$ is
(A) $(3 \mathrm{v} / 2)$
(B) $(4 \mathrm{v} / 2)$
(C) $6 \mathrm{v}$
(D) $12 \mathrm{v}$

Hast Aggarwal

Numerade Educator

Problem 787

A satellite moves in a circle around the earth, the radius of this circle is equal to one half of the radius of the moon's orbit the satellite completes one revolution in........lunar month
(A) $1 / 2$
(B) $2 / 3$
(C) $2^{-3 / 2}$
(D) $12^{3 / 2}$

Amit Srivastava

Amit Srivastava

Numerade Educator

Problem 788

The additional K.E. to be provided to a satellite of mass $\mathrm{m}$ revolving around a planet of mass $\mathrm{M}$, to transfer it from a circular orbit of radius $\mathrm{R}_{1}$ to another radius $\mathrm{R}_{2}\left(\mathrm{R}_{2}>\mathrm{R}_{1}\right)$ is
(A) $\operatorname{GMm}\left[\left(1 / R_{1}^{2}\right)-\left(1 / R_{2}^{2}\right)\right]$
$\operatorname{GMm}\left[\left(1 / R_{1}\right)-\left(1 / R_{2}\right)\right]$
(C) $2 \mathrm{GMm}\left[\left(1 / \mathrm{R}_{1}\right)-\left(1 / \mathrm{R}_{2}\right)\right]$
(D) $(1 / 2) \mathrm{GMm}\left[\left(1 / \mathrm{R}_{1}\right)-\left(1 / \mathrm{R}_{2}\right)\right]$

Narendra Kumar

Numerade Educator

Problem 789

Rockets are launched in eastward direction to take advantage of
(A) the clear sky on eastern side
(B) the thiner atmosphere on this side
(C) earth's rotation
(D) earth's tilt

Chris Johnson

Numerade Educator

Problem 790

A satellite of mass $\mathrm{m}$ is orbiting close to the surface of the earth (Radius $\mathrm{R}=6400 \mathrm{~km}$ ) has a K.E. $\mathrm{K}$. The corresponding $\mathrm{K} . \mathrm{E}$. of satellite to escape from the earth's gravitational field is
(A) $\mathrm{K}$
(B) $2 \mathrm{~K}$
(C) $\mathrm{mg} \mathrm{R}$
(D) $\mathrm{m} \mathrm{K}$

Narayan Hari

Numerade Educator

Problem 791

A planet moving along an elliptical orbit is closest to the sun at a distance $\mathrm{r}_{1}$ and farthest away at a distance of $\mathrm{r}_{2}$. If $\mathrm{v}_{1}$ and $\mathrm{v}_{2}$ are the liner velocities at these points respectively, then the ratio $\left(\mathrm{v}_{1} / \mathrm{v}_{2}\right)$ is $\ldots \ldots \ldots \ldots$
(A) $\left(\mathrm{r}_{1} / \mathrm{r}_{2}\right)$
(B) $\left(\mathrm{r}_{1} / \mathrm{r}_{2}\right)^{2}$
(C) $\left(\mathrm{r}_{2} / \mathrm{r}_{1}\right)$
(D) $\left(\mathrm{r}_{2} / \mathrm{r}_{1}\right)^{2}$

Narayan Hari

Numerade Educator

Problem 792

The time period $\mathrm{T}$ of the moon of planet Mars $(\mathrm{Mm})$ is related to its orbital radius $\mathrm{R}$ as $(\mathrm{G}=$ Gravitational constant $)$
(A) $\mathrm{T}^{2}=\left[\left(4 \pi^{2} \mathrm{R}^{3}\right) /(\mathrm{GMm})\right]$
(B) $\mathrm{T}^{2}=\left[\left(4 \pi^{2} \mathrm{GR}^{3}\right) /(\mathrm{Mm})\right]$
(C) $T^{2}=\left[\left(2 \pi R^{2} G\right) /(M m)\right]$
(D) $\mathrm{T}^{2}=4 \pi \mathrm{Mm} \mathrm{GR}^{2}$

Narayan Hari

Numerade Educator

Problem 793

A geostationary satellite is orbiting the earth at a height of $5 \mathrm{R}$ above that of surface of the earth. $\mathrm{R}$ being the radius of the earth. The time period of another satellite in hours at a height of $2 \mathrm{R}$ from the surface of earth is $\ldots \ldots \ldots .$ hr
(A) 5
(B) 10
(C) $6 \sqrt{2}$
(D) $6 / \sqrt{2}$

Sachin Rao

Numerade Educator

Problem 794

The figure shows elliptical orbit of a planet $\mathrm{m}$ about the sun
s. the shaded area $\mathrm{SCD}$ is twice the shaded area $\mathrm{SAB}$. If $\mathrm{t}_{1}$ is the time for the planet to move from $\mathrm{C}$ and $\mathrm{D}$ and $\mathrm{t}_{2}$ is the time to move from $\mathrm{A}$ to $\mathrm{B}$ then

Yuva S

Numerade Educator

Problem 795

The period of a satellite in a circular orbit of radius $\mathrm{R}$ is $\mathrm{T}$. the period of another satellite in a circular orbit of radius $4 \mathrm{R}$ is
(A) $4 \mathrm{~T}$
(B) $\mathrm{T} / 4$
(C) $8 \mathrm{~T}$
(D) $\mathrm{T} / 8$

Narayan Hari

Numerade Educator

Problem 796

If the earth is at one- fourth of its present distance from the sun the duration of year will be
(A) half the present Year
(B) one-eight the present year
(C) one-fourth the present year
(D) one-sixth the present year

Ajay Singhal

Numerade Educator

Problem 797

The orbital speed of jupiter is
(A) greater than the orbital speed of earth
(B) less than the orbital speed of earth
(C) equal to the orbital speed of earth
(D) zero

Narayan Hari

Numerade Educator

Problem 798

Kepler's second law regarding constancy of aerial velocity of a palnet is consequence of the law of conservation of
(A) energy
(B) angular Momentum
(C) linear momentum
(D) None of these

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 799

The largest and shortest distance of the earth from the sun are $\mathrm{r}_{1}$ and $\mathrm{r}_{2}$ its distance from the sun when it is at the perpendicular to the major axis of the orbit drawn from the sun
(A) $\left[\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right) / 4\right]$
(B) $\left[\left(\mathrm{r}_{1} \mathrm{r}_{2}\right) /\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)\right]$
(C) $\left[\left(2 r_{1} r_{2}\right) /\left(r_{1}+r_{2}\right)\right]$
(D) $\left[\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right) / 3\right]$

Subash Charan

Numerade Educator

Problem 800

According to keplar, the period of revolution of a planet ( $\mathrm{T}$ ) and its mean distance from the sun (r) are related by the equation
(A) $\mathrm{T}^{3} \mathrm{r}^{3}=$ constant
(B) $\mathrm{T}^{2} \mathrm{r}^{-3}=$ constant
(C) $\mathrm{Tr}^{3}=$ constant
(D) $\mathrm{T}^{2} \mathrm{r}=$ constant

Yuva S

Numerade Educator

Problem 801

A satellite of mass $\mathrm{m}$ is circulating around the earth with constant angular velocity. If radius of the orbit is $\mathrm{R}_{0}$ and mass of earth $\mathrm{M}$, the angular momentum about the center of earth is
(A) $m \sqrt{\left(G M R_{0}\right)}$
(B) $\mathrm{M} \sqrt{\left(\mathrm{GMR}_{\mathrm{o}}\right)}$
(C) $\left.m \sqrt{(G M} / R_{0}\right)$
(D) $\mathrm{M} \sqrt{\left(\mathrm{GM} / \mathrm{R}_{\mathrm{o}}\right)}$

Ajay Singhal

Numerade Educator

Problem 802

The earth $\mathrm{E}$ moves in an elliptical orbit with the sun $\mathrm{s}$ at one of the foci as shown in figure. Its speed of motion will be maximum at a point

Ajay Singhal

Numerade Educator

Problem 803

He period of revolution of planet $\mathrm{A}$ around the sun is 8 times that of $\mathrm{B}$. The distance of A from the sun is how many times greater than that of $\mathrm{B}$ from the sun.
(A) 2
(B) 3
(C) 4
(D) 5

Narayan Hari

Numerade Educator

Problem 804

The earth revolves round the sun in one year. If distance between then becomes double the new period will be years.
(A) $0.5$
(B) $2 \sqrt{2}$
(C) 4
(D) 8

Subash Charan

Numerade Educator

Problem 805

The maximum and minimum distance of a comet from the sun are $8 \times 10^{12} \mathrm{~m}$ and $1.6 \times 10^{12} \mathrm{~m} .$ If its velocity when nearest to the sun is $60 \mathrm{~ms}^{-1}$, What will be its velocity in $\mathrm{ms}^{-1}$ when it is farthest?
(A) 6
(B) 12
(C) 60
(D) 112

Hast Aggarwal

Numerade Educator

Problem 806

The period of moon's rotation around th earth is nearly 29 days. If moon's mass were 2 fold its present value and all other things remained unchanged the period of moon's rotation would be nearly
(A) $29 \sqrt{2}$
(B) $29 \sqrt{2}$
(C) $29 \times 2$
(D) 29

Linda Winkler

Numerade Educator

Problem 807

If the velocity of planet is given by $\mathrm{U}=\mathrm{G}^{\mathrm{a}} \mathrm{M}^{\mathrm{b}} \mathrm{R}^{\mathrm{c}}$ then
(A) $a=1 / 3 \quad b=1 / 3$
$c=-1 / 3$
(B) a $=1 / 2 \quad \mathrm{~b}=1 / 2 \quad \mathrm{c}=-1 / 2$
$\begin{array}{ll}\text { (C) } a=1 / 2 & \text { b } & =-1 / 2 & c=1 / 2\end{array}$
(D) $a=1 / 2 \quad$ b $=-1 / 2 \quad c=-1 / 2$

Ajay Singhal

Numerade Educator

Problem 808

The radius of orbit of a planet is two times that of earth. The time period of planet is $\ldots \ldots \ldots$ years.
(A) $4.2$
(B) $2.8$
(C) $5.6$
(D) $8.4$

Narayan Hari

Numerade Educator

Problem 809

If $\mathrm{r}$ denotes the distance between the sun and the earth, then the angular momentum of the earth around the sun is proportional to
(A) $1^{3 / 2}$
(B) $\mathrm{r}$
(C) $r^{1 / 2}$
(D) $r^{2}$

Narayan Hari

Numerade Educator

Problem 810

What does not change in the field of central force
(A) potential energy
(B) Kinetic energy
(C) linear momentum
(D) Angular momentum

Dheeraj Sharma

Numerade Educator

Problem 811

A thin uniform annular disc (See figure) of mass $\mathrm{M}$ has outer radius $4 \mathrm{R}$ and inner radius $3 \mathrm{R}$. The work required to take a unit mass from point $\mathrm{P}$ on its axis to infinity is $\ldots \ldots \ldots$
(A) $[(2 \mathrm{GM}) /(7 \mathrm{R})](4 \sqrt{2}-5)$
(B) $-[(2 \mathrm{GM}) /(7 \mathrm{R})](4 \sqrt{2}-5)$
(C) (GM / 4R)
(D) $[(2 \mathrm{GM}) /(5 \mathrm{R})](\sqrt{2}-1)$

Ajay Singhal

Numerade Educator

Problem 812

Suppose the gravitational force varies inversely as the nth power of distance the time period of planet in circular orbit of radius $\mathrm{R}$ around the sun will be proportional to
(A) $\mathrm{R}^{[(\mathrm{n}+1) / 2]}$
(B) $\mathrm{R}^{[(\mathrm{n}-1) / 2]}$
(C) $\mathrm{R}^{\mathrm{n}}$
(D) $\mathrm{R}^{[(\mathrm{n}-1) / 2]}$

Saman Zulfiqar

Numerade Educator

Problem 813

If the radius of the earth were to shrink by $1 \%$ its mass remaining the same, the acceleration due to gravity on the earth's surface would
(A) decrease by $2 \%$
(B) remain Unchanged
(C) increase by $2 \%$
(D) increases by $1 \%$

Subash Charan

Numerade Educator

Problem 814

A body of mass $\mathrm{m}$ is taken from earth surface to the height $\mathrm{h}$ equal to radius of earth, the increase in potential energy will be
(A) $\operatorname{mg} R$
(B) $(1 / 2) \mathrm{mgR}$
(C) $2 \mathrm{mg} \mathrm{R}$
(D) $(1 / 4) \mathrm{mgR}$

Hast Aggarwal

Numerade Educator

Problem 815

An artificial satellite moving in a circular orbit around earth has a total (kinetic + potential energy) $E_{0}$, its potential energy is
(A) $-\mathrm{E}_{0}$
(B) $1.5 \mathrm{E}_{0}$
(C) $2 \mathrm{E}_{0}$
(D) $\mathrm{E}_{0}$

Narayan Hari

Numerade Educator

Problem 816

Two bodies of masses $m_{1}$ and $m_{2}$ are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual a gravitational attraction Their relative velocity of approach at separation distance $\mathrm{r}$ between them is
(A) $\left[\left\{2 \mathrm{G}\left(\mathrm{m}_{1}-\mathrm{m}_{2}\right)\right\} / \mathrm{r}\right]^{-1 / 2}$
(B) $\left[\left\{2 \mathrm{G}\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right)\right\} / \mathrm{r}\right]^{1 / 2}$
(C) $\left[\mathrm{r} /\left\{2 \mathrm{G}\left(\mathrm{m}_{1} \mathrm{~m}_{2}\right)\right\} / \mathrm{r}\right]^{1 / 2}$
(D) $\left[\left(2 \mathrm{Gm}_{1} \mathrm{~m}_{2}\right) / \mathrm{r}\right]^{1 / 2}$

Saman Zulfiqar

Numerade Educator

Problem 817

A geostationary satellite orbits around the earth in a circular orbit of radius $36000 \mathrm{~km}$ the time period of a satellite orbiting a few hundred kilometers above the earth's surface (Rearth $=6400 \mathrm{~km}$ ) will approximately be $=\ldots \ldots \ldots$ h
(A) $1 / 2$
(B) 1
(C) 2
(D) 4

Hast Aggarwal

Numerade Educator

Problem 818

Direction (Read the following questions and choose)
(A) If both Assertion and Reason are true and the Reason is correct explanation of assertion
(B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion
(C) If Assertion is true, but the Reason is false
(D) If Assertion is false, but the Reason is true
Assertion: The value of acc. due to gravity $(\mathrm{g})$ does not depend upon mass of the body Reason: This follows from $\mathrm{g}=\left[(\mathrm{GM}) / \mathrm{R}^{2}\right]$, where $\mathrm{M}$ is mass of planet (earth) and $\mathrm{R}$ is radius of planet (earth)
(a) $\mathrm{A}$
(b) $\mathrm{B}$
(c) $\mathrm{C}$
(d) D

Vysakh M

Numerade Educator

Problem 819

Direction (Read the following questions and choose)
(A) If both Assertion and Reason are true and the Reason is correct explanation of assertion
(B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion
(C) If Assertion is true, but the Reason is false
(D) If Assertion is false, but the Reason is true
Assertion : Unit of gravitational field intensity is $\mathrm{N} / \mathrm{kg}$ or $\mathrm{ms}^{-2}$ Reason: Gravitational field intensity $[$ Force $) /($ mass $)]=(\mathrm{N} / \mathrm{kg})=\left[\left(\mathrm{kg} \cdot \mathrm{m} / \mathrm{sec}^{2}\right) / \mathrm{kg}\right]=\mathrm{ms}^{-2}$
(a) $\mathrm{A}$
(b) $\mathrm{B}$
(c) $\mathrm{C}$
(d) D

Narayan Hari

Numerade Educator

Problem 820

Direction (Read the following questions and choose)
(A) If both Assertion and Reason are true and the Reason is correct explanation of assertion
(B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion
(C) If Assertion is true, but the Reason is false
(D) If Assertion is false, but the Reason is true
Assertion: The time period of a geostationary satellite is 24 hours Reason: Such a satellite must have the same time period as the time taken by the earth to complete one revolution about its axis
(a) $\mathrm{A}$
(b) B
(c) $\mathrm{C}$
(d) D

Hast Aggarwal

Numerade Educator

Problem 821

Direction (Read the following questions and choose)
(A) If both Assertion and Reason are true and the Reason is correct explanation of assertion
(B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion
(C) If Assertion is true, but the Reason is false
(D) If Assertion is false, but the Reason is true
Assertion: Even when orbit of a satellite is elliptical, its plane of rotation passes through the center of earth Reason: This is in accordance with the principle of conservation of angular momentum
(a) $\mathrm{A}$
(b) B
(c) $\mathrm{C}$
(d) $\mathrm{D}$

Vysakh M

Numerade Educator

Problem 822

Direction (Read the following questions and choose)
(A) If both Assertion and Reason are true and the Reason is correct explanation of assertion
(B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion
(C) If Assertion is true, but the Reason is false
(D) If Assertion is false, but the Reason is true
Assertion: The time Period of pendulum, on a satellite orbiting the earth is infinity Reason : Time period of a pendulum is inversely proportional to $\sqrt{g}$
(a) $\mathrm{A}$
(b) $\mathrm{B}$
(c) $\mathrm{C}$
(d) $D$

Vysakh M

Numerade Educator

Problem 823

Direction (Read the following questions and choose)
(A) If both Assertion and Reason are true and the Reason is correct explanation of assertion
(B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion
(C) If Assertion is true, but the Reason is false
(D) If Assertion is false, but the Reason is true
Assertion: The escape velocity on the surface of a planet of the same mass but $(1 / 4)$ times the radius of earth is $5.6 \mathrm{kms}^{-1}$ Reason : The escape velocity $\left.\mathrm{V}_{\mathrm{e}}=\sqrt{(} 2 \mathrm{gR}\right)$
(a) $\mathrm{A}$
(b) $\mathrm{B}$
(c) $\mathrm{C}$
(d) D

Vysakh M

Numerade Educator

Problem 824

Direction (Read the following questions and choose)
(A) If both Assertion and Reason are true and the Reason is correct explanation of assertion
(B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion
(C) If Assertion is true, but the Reason is false
(D) If Assertion is false, but the Reason is true
Assertion: The comet does not obey kepler's law of planetary motion Reason: The comet does not have elliptical orbit
(a) $\mathrm{A}$
(b) $\mathrm{B}$
(c) $\mathrm{C}$
(d) D

Prem Bijarniya

Numerade Educator

Problem 825

Direction (Read the following questions and choose)
(A) If both Assertion and Reason are true and the Reason is correct explanation of assertion
(B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion
(C) If Assertion is true, but the Reason is false
(D) If Assertion is false, but the Reason is true
Assertion: The square of the period of revolution of a planet is proportional to the cube of its distance from the sun. Reason: Sun's gravitational field is inversely proportional to the square of its distance from the planet
(a) $\mathrm{A}$
(b) $\mathrm{B}$
(c) $\mathrm{C}$
(d) D

Vysakh M

Numerade Educator

Problem 826

Direction (Read the following questions and choose)
(A) If both Assertion and Reason are true and the Reason is correct explanation of assertion
(B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion
(C) If Assertion is true, but the Reason is false
(D) If Assertion is false, but the Reason is true
Assertion : Space ship while entering the earth's atmosphere is likely to catch fire Reason : (a) A 10 Assertion Temperature of upper atmosphere is very high
(a) $\mathrm{A}$
(b) B
(c) $\mathrm{C}$
(d) D

Vysakh M

Numerade Educator

Problem 827

Direction (Read the following questions and choose)
(A) If both Assertion and Reason are true and the Reason is correct explanation of assertion
(B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion
(C) If Assertion is true, but the Reason is false
(D) If Assertion is false, but the Reason is true
Assertion: The earth is slowing down and as a result the moon is coming nearer to it The angular momentum of earth-moon system is not conserved
(a) $\mathrm{A}$
(b) B
(c) $\mathrm{C}$
(d) D

Vysakh M

Numerade Educator

Problem 828

If a smooth tunnel is dug across a diameter of earth and a particle is related from the surface of earth, the particle oscillates simple harmonically along it.
(1) Time period of the particle is not equal to
(A) $2 \pi \sqrt{(R / g)}$
(B) $[2 \pi / \sqrt{(} \mathrm{GM})] \mathrm{R}^{3 / 2}$
(C) $84.0 \mathrm{~min}$
(D) None of these
(2) Maximum speed of these
(A) $\sqrt{[}(2 \mathrm{GM}) / \mathrm{R}]$
(B) $\sqrt{[}(\mathrm{GM}) / \mathrm{R}]$
(D) $\sqrt{[}(\mathrm{GM}) /(2 \mathrm{R})]$

Yuva S

Numerade Educator

Problem 829

When a particle is projected from the surface of earth, it mechanical energy and angular momentum about center of earth at all time is constant
(i) A particle of mass $\mathrm{m}$ is projected from the surface of earth with velocity $\mathrm{V}_{0}$ at angle $\theta$ with horizontal suppose $\mathrm{h}$ be the maximum height of particle from surface of earth and $\mathrm{v}$ its speed at that point them $\mathrm{V}$ is
(A) $\mathrm{V}_{0} \cos \theta$
$(\mathrm{B})>\mathrm{V}_{0} \cos \theta$
(C) $<\mathrm{V}_{0} \cos \theta$
(D) zero
(ii) Maximum height h of the particle is
$(\mathrm{A})=\left[\left(\mathrm{V}_{0}^{2} \sin ^{2} \theta\right) / 2 \mathrm{~g}\right]$
(B) $>\left[\left(\mathrm{V}_{0}^{2} \sin ^{2} \theta\right) / 2 \mathrm{~g}\right]$
$(\mathrm{C})<\left[\left(\mathrm{V}_{0}^{2} \sin ^{2} \theta\right) / 2 \mathrm{~g}\right]$
(D) can be greater than or less than $\left[\left(\mathrm{V}_{0}^{2} \sin ^{2} \theta\right) / 2 \mathrm{~g}\right]$

Hunza Gilgit

Numerade Educator

Problem 830

A solid sphere of mass $\mathrm{M}$ and radius $\mathrm{R}$ is surrounding by a spherical shell of same mass $\mathrm{M}$ and radius $2 \mathrm{R}$ as shown. A small particle of mass $m$ is released from rest from a height $(\mathrm{h}<<\mathrm{R})$ above the shell there is a hole in the shell.
(i) in what time will it enter the hole at $\mathrm{A}$
(A) $\left[\left(2 \sqrt{\mathrm{hR}}^{2}\right) /(\mathrm{GM})\right]$
(B) $\left.\sqrt{[}\left(2 \mathrm{hR}^{2}\right) /(\mathrm{GM})\right]$
(D) None of these(ii) What time will it take to move from $\mathrm{A}$ to $\mathrm{B}$ ?
$(\mathrm{A})=\left[\mathrm{R}^{2} /(\sqrt{\mathrm{GMh}})\right]$
(B) $>\left[\mathrm{R}^{2} /(\sqrt{\mathrm{G} M h})\right]$
$(\mathrm{C})<\left[\mathrm{R}^{2} /(\sqrt{\mathrm{G} M h})\right]$
(D) None of these
(iii) with what approximate speed will it collide at $\mathrm{B}$ ?
(A) $\sqrt{[}(2 \mathrm{GM}) / \mathrm{R}]$
(B) $\sqrt{[}(3 \mathrm{GM}) /(2 \mathrm{R})]$
(C) $\sqrt{[}(\mathrm{GM}) /(2 \mathrm{R})]$
(D) $\sqrt{(\mathrm{GM} / \mathrm{R})}$

Yuva S

Numerade Educator

Problem 831

A planet is revolving round the sun in elliptical orbit. Velocity at perigee position (nearest) is $\mathrm{v}_{1} \mid$ and at apogee position (farthest) is $\mathrm{v}_{2}$ Both these velocities are perpendicular to the joining center of sun and planet $r$ is the minimum distance and $\mathrm{r}_{2}$ the maximum distance.
(1) when the planet is at perigee position, it wants to revolve in a circular orbit by itself. For this value of $\mathrm{G}$
(A) Should increase
(B) Should decrease
(C) data is insufficient
(D) will not depend on the value of $\mathrm{G}$
(2) At apogee position suppose speed of planer is slightly decreased from $\mathrm{v}_{2}$, then what will happen to minimum distance $r_{1}$ in the subsequent motion
(A) $r_{1}$ and $r_{2}$ both will decreases
(B) $\mathrm{r}_{1}$ and $\mathrm{r}_{2}$ both will increases
(C) $\mathrm{r}_{2}$ will remain as it is while $\mathrm{r}_{1}$ will increase
(D) $\mathrm{r}_{2}$ will remain as it is while $\mathrm{r}_{1}$ will decrease

Narayan Hari

Numerade Educator

Problem 832

Gravitational potential at any point inside a spherical shall is uniform and is given by $-(\mathrm{GM} / \mathrm{R})$ where $\mathrm{M}$ is the mass of shell and $\mathrm{R}$ its radius. At the center solid sphere, potential is $[-\{(3 \mathrm{GM}) /(2 \mathrm{R})\}]$(1) There is a concentric hole of radius $\mathrm{R}$ in a solid sphere of radius $2 \mathrm{R}$ mass of the remaining portion is $\mathrm{M}$ what is the gravitational at center?
(A) $-[(3 \mathrm{GM}) / 7 \mathrm{R}]$
(B) $-[(5 \mathrm{GM}) / 7 \mathrm{R}]$
(C) $-[(7 \mathrm{GM}) / 14]$
(D) $-[(9 \mathrm{GM}) /(14 \mathrm{R})]$

Subash Charan

Numerade Educator

Problem 833

On the surface of earth acceleration due to gravity is $\mathrm{g}$ and gravitational potential is $\mathrm{V}$ match the followingTable - 1 Table $-2$
(A) At height $\mathrm{h}=\mathrm{R}$ value of $\mathrm{g}$
(P) decrease by a factor $(1 / 4)$
(B) At depth $\mathrm{h}=(\mathrm{R} / 2)$
(Q) decrease by a factor $(1 / 2)$
(C) At height $\mathrm{h}=\mathrm{R}$ value of $\mathrm{v}$
(R) increase by a factor $(11 / 8)$
(D) At depth $\mathrm{h}=(\mathrm{R} / 2)$ value of $\mathrm{v}$
(S) increase by a factor 2
(T) None

Hafiz Shahzaib

Numerade Educator

Problem 834

Density of planet is two times the density of earth Radius of this to earth) Match the following
Table - 1 Table - 2
(A) Acceleration due to gravity on this
(P) Half planet's surface
(B) Gravitational potential on the surface
(Q) same
(C) Gravitational potential at centre
(R) Two times
(D) Gravitational field strength at centre
(S) four times

Supratim Pal

Numerade Educator

Problem 835

let $\mathrm{V}$ and $\mathrm{E}$ denote the gravitational potential and gravitational field at a point. Then the match the following
$\begin{array}{ll}\text { Table }-1 & \text { Table }-2\end{array}$
(A) $\mathrm{E}=0, \mathrm{~V}=0$
(P) At center of spherical shell
(B) $\mathrm{E} \neq 0, \mathrm{~V}=0$
(Q) At center of solid sphere
(C) $\mathrm{V} \neq 0, \mathrm{E}=0$
(R) at centre of circular ring
(D) $\mathrm{V} \neq 0, \mathrm{E} \neq 0$
(S) At centre of two point masses of equal magnitude
(T) None

Hafiz Shahzaib

Numerade Educator

Problem 836

Match the following
Table-1 Table-2
(A) time period of an earth
(P) Independent of mass of Satellite in circular orbit $\quad$ satellite
(B) Orbital velocity of satellite
(Q) independent of radius of orbit
(C) Mechanical energy
(R) independent of mass of earth
(S) none

Hafiz Shahzaib

Numerade Educator

Problem 837

Match the following
Table-1 $\quad$ Table-2
(A) kinetic energy
(P) $[(-\mathrm{GMm}) /(2 \mathrm{r})]$
(B) Potential energy
(Q) $\sqrt{(\mathrm{GM} / \mathrm{r})}$
(C) Total energy
(R) - [(GMm) / r]
(D) orbital velocity
(S) $[(\mathrm{GMm}) /(2 \mathrm{r})]$
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Hafiz Shahzaib

Numerade Educator