Genius Physics (Class 11) - For IIT-JEE and CBSE

Pradeep Kshetrapal

Chapter 8

Gravitation - all with Video Answers

Educators

Chapter Questions

Problem 1

The gravitational force between two objects does not depend on
(a) Sum of the masses
(b) Product of the masses
(c) Gravitational constant
(d) Distance between the masses

Hast Aggarwal

Hast Aggarwal

Numerade Educator

Problem 2

Mass $M$ is divided into two parts $x M$ and $(1-x) M$. For a given separation, the value of $x$ for which the gravitational attraction between the two pieces becomes maximum is
(a) $\frac{1}{2}$
(b) $\frac{3}{5}$
(c) 1
(d) 2

Darmendar Jain

Numerade Educator

Problem 3

The mass of the moon is about $1.2 \%$ of the mass of the earth. Compared to the gravitational force the earth exerts on the moon, the gravitational force the moon exerts on earth
(a) Is the same
(b) Is smaller
(c) Is greater
(d) Varies with its phase

Hast Aggarwal

Numerade Educator

Problem 4

Three identical point masses, each of mass $1 \mathrm{~kg}$ lie in the $x-y$ plane at points $(0,0),(0,0.2 m)$ and (o.2m, o). The net gravitational force on the mass at the origin is
(a) $1.67 \times 10^{-9}(\hat{j}+\hat{j}) N$
(b) $3.34 \times 10^{-10}(\hat{i}+\hat{j}) N$
(c) $1.67 \times 10^{-9}(\hat{i}-\hat{j}) N$
(d) $3.34 \times 10^{-10}(\hat{i}+\hat{j}) N$

Hast Aggarwal

Numerade Educator

Problem 5

Four particles of masses $m, 2 m, 3 m$ and $4 m$ are kept in sequence at the corners of a square of side $a$. The magnitude of gravitational force acting on a particle of mass $m$ placed at the centre of the square will be
(a) $\frac{24 m^{2} G}{a^{2}}$
(b) $\frac{6 m^{2} G}{a^{2}}$
(c) $\frac{4 \sqrt{2} G m^{2}}{a^{2}}$
(d) Zero

Hast Aggarwal

Numerade Educator

Problem 6

Acceleration due to gravity on moon is $1 / 6$ of the acceleration due to gravity on earth. If the ratio of densities of earth $\left(\rho_{m}\right)$ and moon $\left(\rho_{e}\right)$ is $\left(\frac{\rho_{e}}{\rho_{m}}\right)=\frac{5}{3}$ then radius of moon $R_{m}$ in terms of $R_{e}$ will be
(a) $\frac{5}{18} R_{e}$
(b) $\frac{1}{6} R_{e}$
(c) $\frac{3}{18} R_{e}$
(d) $\frac{1}{2 \sqrt{3}} R_{e}$

Hast Aggarwal

Numerade Educator

Problem 7

A spherical planet far out in space has a mass $M_{0}$ and diameter $D_{0}$. A particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to
(a) $G M_{0} / D_{0}^{2}$
(b) $4 m G M_{0} / D_{0}^{2}$
(c) $4 G M_{0} / D_{0}^{2}$
(d) $G m M_{0} / D_{0}^{2}$

Hast Aggarwal

Numerade Educator

Problem 8

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

Narendra Kumar

Numerade Educator

Problem 9

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 [IIT-JEE 1981; CPMT 1981; MP PMT 1996, 97; Roorkee 1992;
(a) Decrease by $2 \%$
(b) Remain unchanged
(c) Increase by $2 \%$
(d) Increase by $1 \%$

Hast Aggarwal

Numerade Educator

Problem 10

Mass of moon is $7.34 \times 10^{22} \mathrm{~kg}$. If the acceleration due to gravity on the moon is $1.4 \mathrm{~m} / \mathrm{s}^{2}$, the radius of the moon is $\left(G=6.667 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}\right)$
(a) $0.56 \times 10^{4} \mathrm{~m}$
(b) $1.87 \times 10^{6} \mathrm{~m}$
(c) $1.92 \times 10^{6} \mathrm{~m}$
(d) $1.01 \times 10^{8} \mathrm{~m}$

Hast Aggarwal

Numerade Educator

Problem 11

A planet has mass $1 / 10$ of that of earth, while radius is $1 / 3$ that of earth. If a person can throw a stone on earth surface to a height of $90 m$, then he will be able to throw the stone on that planet to a height
(a) $9 \mathrm{om}$
(b) $40 m$
(c) $100 m$
(d) $45 \mathrm{~m}$

Hast Aggarwal

Numerade Educator

Problem 12

The radii of two planets are respectively $R_{1}$ and $R_{2}$ and their densities are respectively $\rho_{1}$ and $\rho_{2}$. The ratio of the accelerations due to gravity at their surfaces is
(a) $g_{1}: g_{2}=\frac{\rho_{1}}{R_{1}^{2}}: \frac{\rho_{2}}{R_{2}^{2}}$
(b) $g_{1}: g_{2}=R_{1} R_{2}: \rho_{1} \rho_{2}$
(c) $g_{1}: g_{2}=R_{1} \rho_{2}: R_{2} \rho_{1}$
(d) $g_{1}: g_{2}=R_{1} \rho_{1}: R_{2} \rho_{2}$

Hast Aggarwal

Numerade Educator

Problem 13

Where will it be profitable to purchase $1 \mathrm{~kg}$ sugar (by spring balance)
(a) At poles
(b) At equator
(c) At $45^{\circ}$ latitude
(d) At $40^{\circ}$ latitude

Hast Aggarwal

Numerade Educator

Problem 14

Force of gravity is least at
(a) The equator
(b) The poles
(c) A point in between equator and any pole
(d) None of these

Hast Aggarwal

Numerade Educator

Problem 15

The acceleration of a body due to the attraction of the earth (radius $R$ ) at a distance $2 R$ from the surface of the earth is ( $g=$ acceleration due to gravity at the surface of the earth)
(a) $\frac{g}{9}$
(b) $\frac{g}{3}$
(c) $\frac{g}{4}$
(d) $g$

Hast Aggarwal

Numerade Educator

Problem 16

The height of the point vertically above the earth's surface, at which acceleration due to gravity becomes $1 \%$ of its value at the surface is (Radius of the earth $=R$ )
(a) $8 R$
(b) $9 R$
(c) $10 R$
(d) $20 R$

Hast Aggarwal

Numerade Educator

Problem 17

At surface of earth weight of a person is $72 N$ then his weight at height $R / 2$ from surface of earth is ( $R$ = radius of earth)
(a) $28 N$
(b) $16 N$
(c) $3^{2} N$
(d) $72 N$

Hast Aggarwal

Numerade Educator

Problem 18

If the distance between centres of earth and moon is $D$ and the mass of earth is 81 times the mass of moon, then at what distance from centre of earth the gravitational force will be zero
(a) $D / 2$
(b) $2 D / 3$
(c) $4 D / 3$
(d) $9 D / 10$

Hast Aggarwal

Numerade Educator

Problem 19

Weight of a body of mass $m$ decreases by $1 \%$ when it is raised to height $h$ above the earth's surface. If the body is taken to a depth h in a mine, change in its weight is
(a) $2 \%$ decrease
(b) $0.5 \%$ decrease
(c) $1 \%$ increase
(d) $0.5 \%$ increase

Ajay Singhal

Numerade Educator

Problem 20

The depth at which the effective value of acceleration due to gravity is $\frac{g}{4}$ is ( $R=$ radius of the earth)
(a) $R$
(b) $\frac{3 R}{4}$
(c) $\frac{R}{2}$
(d) $\frac{R}{4}$

Hast Aggarwal

Numerade Educator

Problem 21

Assuming earth to be a sphere of a uniform density, what is the value of gravitational acceleration in a mine $100 \mathrm{~km}$ below the earth's surface (Given $R=6400 \mathrm{~km}$ )
(a) $9.66 \mathrm{~m} / \mathrm{s}^{2}$
(b) $7.64 \mathrm{~m} / \mathrm{s}^{2}$
(c) $5.06 \mathrm{~m} / \mathrm{s}^{2}$
(d) $3.10 \mathrm{~m} / \mathrm{s}^{2}$

Hast Aggarwal

Numerade Educator

Problem 22

The depth $d$ at which the value of acceleration due to gravity becomes $\frac{1}{n}$ times the value at the surface, is $[R=$ radius of the earth $]$
(a) $\frac{R}{n}$
(b) $R\left(\frac{n-1}{n}\right)$
(c) $\frac{R}{n^{2}}$
(d) $R\left(\frac{n}{n+1}\right)$

Subash Charan

Numerade Educator

Problem 23

The angular velocity of the earth with which it has to rotate so that acceleration due to gravity on $60^{\circ}$ latitude becomes zero is (Radius of earth $=6400 \mathrm{~km}$. At the poles $g=10 \mathrm{~ms}^{-2}$ )
(a) $2.5 \times 10^{-3} \mathrm{rad} / \mathrm{sec}$
(b) $5.0 \times 10^{-1} \mathrm{rad} / \mathrm{sec}$
(c) $10 \times 10^{1} \mathrm{rad} / \mathrm{sec}$
(d) $7.8 \times 10^{-2} \mathrm{rad} / \mathrm{sec}$

Hast Aggarwal

Numerade Educator

Problem 24

If earth stands still what will be its effect on man's weight
(a) Increases
(b) Decreases
(c) Remains same
(d) None of these

Hast Aggarwal

Numerade Educator

Problem 25

If the angular speed of earth is increased so much that the objects start flying from the equator, then the length of the day will be nearly
(a) $1.5$ hours
(b) 8 hours
(c) 18 hours
(d) 24 hours

Hast Aggarwal

Numerade Educator

Problem 26

Gravitational mass is proportional to gravitational
(a) Field
(b) Force
(c) Intensity
(d) All of these

Hast Aggarwal

Numerade Educator

Problem 27

The ratio of the inertial mass to gravitational mass is equal to
(a) $1 / 2$
(b) 1
(c) 2
(d) No fixed number

Hast Aggarwal

Numerade Educator

Problem 28

Knowing that mass of Moon is $\frac{M}{81}$ where $M$ is the mass of Earth, find the distance of the point where gravitational field due to Earth and Moon cancel each other, from the Moon. Given that distance between Earth and Moon is $60 R$. Where $R$ is the radius of Earth
(a) $2 R$
(b) $4 R$
(c) $6 \mathrm{R}$
(d) $8 R$

Hast Aggarwal

Numerade Educator

Problem 29

The gravitational potential in a region is given by $V=(3 x+4 y+12 z) J / k g$. The modulus of the gravitational field at $(x=1, y=0, z=3)$ is
(a) $20 \mathrm{~N} \mathrm{~kg}^{-1}$
(b) $13 \mathrm{~N} \mathrm{~kg}^{-1}$
(c) $12 \mathrm{~N} \mathrm{~kg}^{-1}$
(d) $5 \mathrm{~N} \mathrm{~kg}^{-1}$

Hast Aggarwal

Numerade Educator

Problem 30

The magnitudes of the gravitational field at distance $r_{1}$ and $r_{2}$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $F_{1}$ and $F_{2}$ respectively. Then
(a) $\frac{F_{1}}{F_{2}}=\frac{r_{1}}{r_{2}}$ if $r_{1}<R$ and $r_{2}<R$
(b) $\frac{F_{1}}{F_{2}}=\frac{r_{2}^{2}}{r_{1}^{2}}$ if $r_{1}>R$ and $r_{2}>R$
(c) $\frac{F_{1}}{F_{2}}=\frac{r_{1}}{r_{2}}$ if $r_{1}>R$ and $r_{2}>R$
(d) $\frac{F_{1}}{F_{2}}=\frac{r_{1}^{2}}{r_{2}^{2}}$ if $r_{1}<R$ and $r_{2}<R$

Hast Aggarwal

Numerade Educator

Problem 31

Infinite bodies, each of mass $3 \mathrm{~kg}$ are situated at distances $1 \mathrm{~m}, 2 \mathrm{~m}, 4 \mathrm{~m}, 8 m \ldots \ldots .$ respectively on $x$-axis. The resultant intensity of gravitational field at the origin will be
(a) $G$
(b) $2 G$
(c) $3 G$
(d) $4 G$

Hast Aggarwal

Numerade Educator

Problem 32

Two concentric shells of mass $M_{1}$ and $M_{2}$ are having radii $r_{1}$ and $r_{2}$. Which of the following is the correct expression for the gravitational field on a mass $m$.
(a) $I=\frac{G\left(M_{1}+M_{2}\right)}{r^{2}}$ for $r<r_{1}$
(b) $I=\frac{G\left(M_{1}+M_{2}\right)}{r^{2}}$ for $r<r_{2}$
(c) $I=G \frac{M_{2}}{r^{2}}$ for $r_{1}<r<r_{2}$
(d) $I=\frac{G M_{1}}{r^{2}}$ for $r_{1}<r<r_{2}$

Hast Aggarwal

Numerade Educator

Problem 33

A spherical shell is cut into two pieces along a chord as shown in the figure. $P$ is a point on the plane of the chord. The gravitational field at $P$ due to the upper part is $I_{1}$ and that due to the lower part is $I_{2}$. What is the relation between them
(a) $I_{1}>I_{2}$
(b) $I_{1}<I_{2}$
(c) $I_{1}=I_{2}$
(d) No definite relation

Hast Aggarwal

Numerade Educator

Problem 34

A uniform ring of mass $m$ is lying at a distance $1.73 a$ from the centre of a sphere of mass $M$ just over the sphere where $a$ is the small radius of the ring as well as that of the sphere. Then gravitational force exerted is
(a) $\frac{G M m}{8 a^{2}}$
(b) $\frac{G M m}{(1.73 a)^{2}}$
(c) $\sqrt{3} \frac{G M m}{a^{2}}$
(d) $1.73 \frac{G M m}{8 a^{2}}$

Hast Aggarwal

Numerade Educator

Problem 35

In some region, the gravitational field is zero. The gravitational potential in this region
(a) Must be variable
(b) Must be constant
(c) Cannot be zero
(d) Must be zero

Hast Aggarwal

Numerade Educator

Problem 36

The gravitational field due to a mass distribution is $E=K / x^{3}$ in the $x$ - direction ( $K$ is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance $x$ is
(a) $K / x$
(b) $K / 2 x$
(c) $K / x^{2}$
(d) $K / 2 x^{2}$

Hast Aggarwal

Numerade Educator

Problem 37

The intensity of gravitational field at a point situated at a distance of $8000 \mathrm{~km}$ from the centre of the earth is $6 \mathrm{~N} / \mathrm{kg}$. The gravitational potential at that point is $-$ (in Joule / $\mathrm{kg}$ )
(a) $8 \times 10^{66}$
(b) $2.4 \times 10^{3}$
(c) $4.8 \times 10^{7}$
(d) $6.4 \times 10^{14}$

Hast Aggarwal

Numerade Educator

Problem 38

The gravitational potential due to the earth at infinite distance from it is zero. Let the gravitational potential at a point $P$ be $-5 J / k g$. Suppose, we arbitrarily assume the gravitational potential at infinity to $\mathrm{be}+10 \mathrm{~J} / \mathrm{kg}$, then the gravitational potential at $P$ will be
(a) $-5 \mathrm{~J} / \mathrm{kg}$
(b) $+5 J / k g$
(c) $-15 \mathrm{~J} / \mathrm{kg}$
(d) $+15 J / k g$

Hast Aggarwal

Numerade Educator

Problem 39

An infinite number of point masses each equal to $m$ are placed at $x=1 . x=2, x=4, x=8 \ldots \ldots \ldots$. What is the total gravitational potential at $x=0$
(a) $-G m$
(b) $-2 \mathrm{Gm}$
(c) $-4 \mathrm{Gm}$
(d) $-8 \mathrm{Gm}$

Hast Aggarwal

Numerade Educator

Problem 40

Two bodies of masses $m$ and $M$ are placed a distance $d$ apart. The gravitational potential at the position where the gravitational field due to them is zero is $V$, then
(a) $V=-\frac{G}{d}(m+M)$
(b) $V=-\frac{G m}{d}$
(c) $V=-\frac{G M}{d}$
(d) $V=-\frac{G}{d}(\sqrt{m}+\sqrt{M})^{2}$

Hast Aggarwal

Numerade Educator

Problem 41

Energy required to move a body of mass $m$ from an orbit of radius $2 R$ to $3 R$ is
(a) $\frac{G M m}{12 R^{2}}$
(b) $\frac{G M m}{3 R^{2}}$
(c) $\frac{G M m}{8 R}$
(d) $\frac{G M m}{6 R}$

Hast Aggarwal

Numerade Educator

Problem 42

A body of mass $m \mathrm{~kg}$. starts falling from a point $2 R$ above the earth's surface. Its kinetic energy when it has fallen to a point ' $R$ ' above the earth's surface $[R$-Radius of earth, $M$-Mass of earth, $G$-Gravitational constant]
(a) $\frac{1}{2} \frac{G M m}{R}$
(b) $\frac{1}{6} \frac{G M m}{R}$
(c) $\frac{2}{3} \frac{G M m}{R}$
(d) $\frac{1}{3} \frac{G M m}{R}$

Hast Aggarwal

Numerade Educator

Problem 43

A body of mass $m$ is taken from earth surface to the height $h$ equal to radius of earth, the increase in potential energy will be
(a) $m g R$
(b) $\frac{1}{2} m g R$
(c) $2 m g R$
(d) $\frac{1}{4} m g R$

Hast Aggarwal

Numerade Educator

Problem 44

If mass of earth is $M$, radius is $R$ and gravitational constant is $G$, then work done to take $1 \mathrm{~kg}$ mass from earth surface to infinity will be
(a) $\sqrt{\frac{G M}{2 R}}$
(b) $\frac{G M}{R}$
(c) $\sqrt{\frac{2 G M}{R}}$
(d) $\frac{G M}{2 R}$

Hast Aggarwal

Numerade Educator

Problem 45

Three particles each of mass $100 \mathrm{gm}$ are brought from a very large distance to the vertices of an equilateral triangle whose side is $20 \mathrm{~cm}$ in length. The work done will be
(a) $0.33 \times 10^{-11}$ Joule
(b) $-0.33 \times 10^{-11}$ Joule
(c) $1.00 \times 10^{-11}$ Joule
(d) $-1.00 \times 10^{-11}$ Joule

Hast Aggarwal

Numerade Educator

Problem 46

A boy can jump to a height $h$ on ground level. What should be the radius of a sphere of density $d$ such that on jumping on it, he escapes out of the gravitational field of the sphere
(a) $\left[\frac{4 \pi}{3} \frac{G d}{g h}\right]^{1 / 2}$
(b) $\left[\frac{4 \pi}{3} \frac{g h}{G d}\right]^{1 / 2}$
(c) $\left[\frac{3}{4 \pi} \frac{g h}{G d}\right]^{1 / 2}$
(d) $\left[\frac{3}{4 \pi} \frac{G d}{g h}\right]^{1 / 2}$

Hast Aggarwal

Numerade Educator

Problem 47

For a satellite escape velocity is $11 \mathrm{~km} / \mathrm{s}$. If the satellite is launched at an angle of $60^{\circ}$ with the vertical, then escape velocity will be
(a) $11 \mathrm{~km} / \mathrm{s}$
(b) $11 \sqrt{3} \mathrm{~km} / \mathrm{s}$
(c) $\frac{11}{\sqrt{3}} \mathrm{~km} / \mathrm{s}$
(d) $33 \mathrm{~km} / \mathrm{s}$

Hast Aggarwal

Numerade Educator

Problem 48

The escape velocity from the earth is about $11 \mathrm{~km} / \mathrm{s}$. The escape velocity from a planet having twice the radius and the same mean density as the earth, is
(a) $22 \mathrm{~km} / \mathrm{s}$
(b) $11 \mathrm{~km} / \mathrm{s}$
(c) $5.5 \mathrm{~km} / \mathrm{s}$
(d) $15.5 \mathrm{~km} / \mathrm{s}$

Hast Aggarwal

Numerade Educator

Problem 49

A projectile is projected with velocity $k v_{e}$ in vertically upward direction from the ground into the space. $\left(v_{e}\right.$ is escape velocity and $k<1$ ). If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be ( $R=$ radius of earth)
(a) $\frac{R}{k^{2}+1}$
(b) $\frac{R}{k^{2}-1}$
(c) $\frac{R}{1-k^{2}}$
(d) $\frac{R}{k+1}$

Hast Aggarwal

Numerade Educator

Problem 50

If the radius of earth reduces by $4 \%$ and density remains same then escape velocity will
(a) Reduce by $2 \%$
(b) Increase by $2 \%$
(c) Reduce by $4 \%$
(d) Increase by $4 \%$

Hast Aggarwal

Numerade Educator

Problem 51

A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is
(a) $\frac{R}{\left(\frac{g R}{2 V^{2}}-1\right)}$
(b) $R\left(\frac{g R}{2 V^{2}}-1\right)$
(c) $\frac{R}{\left(\frac{2 g R}{V^{2}-1}\right)}$
(d) $R\left(\frac{2 g R}{V^{2}}-1\right)$

Hast Aggarwal

Numerade Educator

Problem 52

A body of mass $m$ is situated at a distance $4 R_{e}$ above the earth's surface, where $R_{e}$ is the radius of earth. How much minimum energy be given to the body so that it may escape
(a) $m g R_{e}$
(b) $2 m g R_{e}$
(c) $\frac{m g R_{c}}{5}$
(d) $\frac{m g R_{e}}{16}$

Hast Aggarwal

Numerade Educator

Problem 53

The distance of a planet from the sun is 5 times the distance between the earth and the sun. The Time period of the planet is
(a) $5^{3 / 2}$ years
(b) $5^{2 / 3}$ years
(c) $5^{1 / 3}$ years
(d) $5^{1 / 2}$ years

Hast Aggarwal

Numerade Educator

Problem 54

In planetary motion the areal velocity of position vector of a planet depends on angular velocity $(\omega)$ and the distance of the planet from sun $(r)$. If so the correct relation for areal velocity is
(a) $\frac{d A}{d t} \propto \omega r$
(b) $\frac{d A}{d t} \propto \omega^{2} r$
(c) $\frac{d A}{d t} \propto \omega r^{2}$
(d) $\frac{d A}{d t} \propto \sqrt{\omega r}$

Hast Aggarwal

Numerade Educator

Problem 55

The planet is revolving around the sun as shown in elliptical path. The correct option is
(a) The time taken in travelling $D A B$ is less than that for $B C D$
(b) The time taken in travelling $D A B$ is greater than that for $B C D$
(c) The time taken in travelling $C D A$ is less than that for $A B C$
(d) The time taken in travelling $C D A$ is greater than that for $A B C$

Hast Aggarwal

Numerade Educator

Problem 56

The distance of Neptune and Saturn from sun are nearly $10^{13}$ and $10^{12}$ meters respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio
(a) $\sqrt{10}$
(b) 100
(c) $10 \sqrt{10}$
(d) $1 / \sqrt{10}$

Hast Aggarwal

Numerade Educator

Problem 57

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 $60 \mathrm{~m} / \mathrm{s}$, what will be its velocity in $\mathrm{m} / \mathrm{s}$ when it is farthest
(a) 12
(b) 60
(c) 112
(d) 6

Hast Aggarwal

Numerade Educator

Problem 58

A satellite $A$ of mass $m$ is at a distance of $r$ from the centre of the earth. Another satellite $B$ of mass $2 m$ is at distance of $2 r$ from the earth's centre. Their time periods are in the ratio of
(a) $1: 2$
(b) $1: 16$
(c) $1: 32$
(d) $1: 2 \sqrt{2}$

Hast Aggarwal

Numerade Educator

Problem 59

A planet moves around the sun. At a given point $P$, it is closed from the sun at a distance $d_{1}$ and has a speed $v_{1} .$ At another point $Q$. when it is farthest from the sun at a distance $d_{2}$, its speed will be [MP PMT $\mathbf{1 9} \mathbf{8}_{7}$ ]
(a) $\frac{d_{1}^{2} v_{1}}{d_{2}^{2}}$
(b) $\frac{d_{2} v_{1}}{d_{1}}$
(c) $\frac{d_{1} v_{1}}{d_{2}}$
(d) $\frac{d_{2}^{2} v_{1}}{d_{1}^{2}}$

Hast Aggarwal

Numerade Educator

Problem 60

Two satellites $A$ and $B$ go round a planet $P$ in circular orbits having radii $4 R$ and $R$ respectively. If the speed of the satellite $A$ is $3 V$, the speed of the satellite $B$ will be
(a) $12 V$
(b) $6 \mathrm{~V}$
(c) $3 / 2 V$
(d) $3 / 2 V$

Hast Aggarwal

Numerade Educator

Problem 61

A satellite is moving around the earth with speed $v$ in a circular orbit of radius $r$. If the orbit radius is decreased by $1 \%$, its speed will
(a) Increase by $1 \%$
(b) Increase by $0.5 \%$
(c) Decrease by $1 \%$
(d) Decrease by o.5\%

Hast Aggarwal

Numerade Educator

Problem 62

If the gravitational force between two objects were proportional to $1 / R$; where $R$ is separation between them, then a particle in circular orbit under such a force would have its orbital speed $v$ proportional to
(a) $1 / R^{2}$
(b) $R^{0}$
(c) $R^{1}$
(d) $1 / R$

Hast Aggarwal

Numerade Educator

Problem 63

The distance between centre of the earth and moon is $384000 \mathrm{~km}$. If the mass of the earth is $6 \times 10^{24} \mathrm{~kg}$ and $G=6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$. The speed of the moon is nearly
(a) $1 \mathrm{~km} / \mathrm{sec}$
(b) $4 \mathrm{~km} / \mathrm{sec}$
(c) $8 \mathrm{~km} / \mathrm{sec}$
(d) $11.2 \mathrm{~km} / \mathrm{sec}$

Hast Aggarwal

Numerade Educator

Problem 64

A satellite is launched into a circular orbit of radius ' $R$ ' around earth while a second satellite is launched into an orbit of radius $1.02 R$. The percentage difference in the time periods of the two satellites is
(a) $0.7$
(b) $1.0$
(c) $1.5$
(d) 3

Hast Aggarwal

Numerade Educator

Problem 65

Periodic time of a satellite revolving above Earth's surface at a height equal to $R$, where $R$ the radius of Earth, is [ $g$ is acceleration due to gravity at Earth's surface]
(a) $2 \pi \sqrt{\frac{2 R}{g}}$
(b) $4 \sqrt{2} \pi \sqrt{\frac{R}{g}}$
(c) $2 \pi \sqrt{\frac{R}{g}}$
(d) $8 \pi \sqrt{\frac{R}{g}}$

Hast Aggarwal

Numerade Educator

Problem 66

An earth satellite $S$ has an orbit radius which is 4 times that of a communication satellite $C$. The period of revolution of $S$ is
(a) 4 days
(b) 8 days
(c) 16 days
(d) 32 days

Hast Aggarwal

Numerade Educator

Problem 67

One project after deviation from its path, starts moving round the earth in a circular path at radius equal to nine times the radius at earth $R$, its time period will be
(a) $2 \pi \sqrt{\frac{R}{g}}$
(b) $27 \times 2 \pi \sqrt{\frac{R}{g}}$
(c) $\pi \sqrt{\frac{R}{g}}$
(d) $8 \times 2 \pi \sqrt{\frac{R}{g}}$

Hast Aggarwal

Numerade Educator

Problem 68

A satellite $A$ of mass $m$ is revolving round the earth at a height ' $r$ 'from the centre. Another satellite $B$ of mass $2 m$ is revolving at a height $2 r$. The ratio of their time periods will be
(a) $1: 2$
(b) $1: 16$
(c) $1: 32$
(d) $1: 2 \sqrt{2}$

Hast Aggarwal

Numerade Educator

Problem 69

Given radius of earth ' $R$ ' and length of a day 'T' the height of a geostationary satellite is
[G - Gravitational constant, $M$ - Mass of earth]
(a) $\left(\frac{4 \pi^{2} G M}{T^{2}}\right)^{1 / 3}$
(b) $\left(\frac{4 \pi G M}{R^{2}}\right)^{1 / 3}-R$
(c) $\left(\frac{G M T^{2}}{4 \pi^{2}}\right)^{1 / 3}-R$
(d) $\left(\frac{G M T^{2}}{4 \pi^{2}}\right)^{1 / 3}+R$

Hast Aggarwal

Numerade Educator

Problem 70

A satellite is revolving round the earth in circular orbit at some height above surface of earth. It takes $5.26 \times 10^{3}$ seconds to complete a revolution while its centripetal acceleration is $9.92 \mathrm{~m} / \mathrm{s}^{2}$. Height of satellite above surface of earth is (Radius of earth $6.37 \times 10^{6} \mathrm{~m}$ )
(a) $70 \mathrm{~km}$
(b) $120 \mathrm{~km}$
(c) $170 \mathrm{~km}$
(d) $220 \mathrm{~km}$

Hast Aggarwal

Numerade Educator

Problem 71

The orbital angular momentum of a satellite revolving at a distance $r$ from the centre is $L$. If the distance is increased to $16 r$, then new angular momentum will be
(a) $16 L$
(b) $64 L$
(c) $\frac{L}{4}$
(d) $4 L$

Hast Aggarwal

Numerade Educator

Problem 72

Angular momentum of a planet of mass $m$ orbiting around sun is $J$, areal velocity of its radius vector will be
(a) $\frac{1}{2} m J$
(b) $\frac{J}{2 m}$
(c) $\frac{m}{2 . J}$
(d) $\frac{1}{2 m J}$

Hast Aggarwal

Numerade Educator

Problem 73

Potential energy of a satellite having mass ' $m$ ' and rotating at a height of $6.4 \times 10^{6} \mathrm{~m}$ from the earth centre is
(a) $-0.5 \mathrm{mgR}_{e}$
(b) $-m g R_{e}$
(c) $-2 m g R_{e}$
(d) $4 m g R_{e}$

Hast Aggarwal

Numerade Educator

Problem 74

In a satellite if the time of revolution is $T$, then kinetic energy is proportional to
(a) $\frac{1}{T}$
(b) $\frac{1}{T^{2}}$
(c) $\frac{1}{T^{3}}$
(d) $T^{-2 / 3}$

Hast Aggarwal

Numerade Educator

Problem 75

Two satellites are moving around the earth in circular orbits at height $R$ and $3 R$ respectively, $R$ being the radius of the earth, the ratio of their kinetic energies is
(a) 2
(b) 4
(c) 8
(d) 16

Hast Aggarwal

Numerade Educator

Problem 76

The time period of a simple pendulum on a freely moving artificial satellite is
(a) Zero
(b) $2 \mathrm{sec}$
(c) $3 \mathrm{sec}$
(d) Infinite

Hast Aggarwal

Numerade Educator

Problem 77

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 the earth
(d) Less than that on the earth

Hast Aggarwal

Numerade Educator

Problem 78

A ball is dropped from a spacecraft revolving around the earth at a height of $120 \mathrm{~km}$. What will happen to the ball
(a) It will continue to move with velocity $v$ along the original orbit of spacecraft
(b) If will move with the same speed tangentially to the spacecraft
(c) It will fall down to the earth gradually
(d) It will go very far in the space

Hast Aggarwal

Numerade Educator

Problem 79

Two particles of equal mass go round a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is
(a) $v=\frac{1}{2 R} \sqrt{\frac{1}{G m}}$
(b) $v=\sqrt{\frac{G m}{2 R}}$
(c) $v=\frac{1}{2} \sqrt{\frac{G m}{R}}$
(d) $v=\sqrt{\frac{4 G m}{R}}$

Hast Aggarwal

Numerade Educator

Problem 80

Two types of balances, the beam balance and the spring balance are commonly used for measuring weight in shops. If we are on the moon, we can continue to use
(a) Only the beam type balance without any change
(b) Only the spring balance without any change
(c) Both the balances without any change
(d) Neither of the two balances without making any change

Hast Aggarwal

Numerade Educator

Problem 81

During a journey from earth to the moon and back, the greatest energy required from the space-ship rockets is to overcome
(a) The earth's gravity at take off
(b) The moon's gravity at lunar landing
(c) The moon's gravity at lunar take off
(d) The point where the pull of the earth and moon are equal but opposite

Hast Aggarwal

Numerade Educator

Problem 82

If the radius of earth contracts $\frac{1}{n}$ of its present value, the length of the day will be approximately
(a) $\frac{24}{n} h$
(b) $\frac{24}{n^{2}} h$
(c) $24 n h$
(d) $24 n^{2} h$

Hast Aggarwal

Numerade Educator

Problem 83

A body released from a height $h$ takes time $t$ to reach earth's surface. The time taken by the same body released from the same height to reach the moon's surface is
(a) $t$
(b) $6 t$
(c) $\sqrt{6} t$
(d) $\frac{t}{6}$

Hast Aggarwal

Numerade Educator

Problem 84

A satellite is revolving round the earth with orbital speed $v_{0}$. If it stops suddenly, the speed with which it will strike the surface of earth would be $\left(v_{e}=\right.$ escape velocity of a particle on earth's surface)
(a) $\frac{v_{e}^{2}}{v_{0}}$
(b) $v_{0}$
(c) $\sqrt{v_{e}^{2}-v_{0}^{2}}$
(d) $\sqrt{v_{e}^{2}-2 v_{0}^{2}}$

Hast Aggarwal

Numerade Educator

Problem 85

The escape velocity for a planet is $v_{e}$. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be
(a) $v_{e}$
(b) $\frac{v_{c}}{\sqrt{2}}$
(c) $\frac{v_{e}}{2}$
(d) Zero

Hast Aggarwal

Numerade Educator

Problem 86

A small body of superdense material, whose mass is twice the mass of the earth but whose size is very small compared to the size of the earth, starts from rest at a height $H<<R$ above the earth's surface, and reaches the earth's surface in time $t$. Then $t$ is equal to
(a) $\sqrt{2 H / g}$
(b) $\sqrt{H / g}$
(c) $\sqrt{2 H / 3 g}$

Hast Aggarwal

Numerade Educator