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A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar

Chapter 8

Properties of Solids and Liquids - all with Video Answers

Educators

Chapter Questions

01:33

Problem 1

The breaking stress of a wire depends on
(A) Material of the wire
(B) Length of the wire
(C) Radius of the wire
(D) Length of the wire

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:08

Problem 2

A wire can be broken by applying a load of $20 \mathrm{~kg}$ wt. The force required to break the wire of twice the diameter is
(A) $20 \mathrm{~kg} \mathrm{wt}$
(B) $5 \mathrm{~kg} \mathrm{wt}$
(C) $80 \mathrm{~kg}$ wt
(D) $160 \mathrm{~kg} \mathrm{wt}$

Darmendar Jain
Darmendar Jain
Numerade Educator
01:19

Problem 3

An elongation of $0.1 \%$ in a wire of cross-sectional area $10^{-6} \mathrm{~m}^{2}$ causes a tension of $100 \mathrm{~N}$. The Young's modulus is
(A) $10^{12} \mathrm{~N} / \mathrm{m}^{2}$
(B) $10^{11} \mathrm{~N} / \mathrm{m}^{2}$
(C) $10^{10} \mathrm{~N} / \mathrm{m}^{2}$
(D) $10^{2} \mathrm{~N} / \mathrm{m}^{2}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:22

Problem 4

A vessel of $1 \times 10^{-3} \mathrm{~m}^{3}$ volume contains oil, when a pressure of $1.2 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ is applied on it, then volume decreases by $0.3 \times 10^{-6} \mathrm{~m}^{3}$. The bulk modulus of oil is
(A) $1 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$
(B) $2 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
(C) $4 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$
(D) $6 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:19

Problem 5

A wooden cylinder floats in water with two-third of its volume inside the water. The density of wood is
(A) $\frac{1000}{3} \mathrm{~kg} / \mathrm{m}^{3}$
(B) $\frac{2000}{3} \mathrm{~kg} / \mathrm{m}^{3}$
(C) $\frac{500}{3} \mathrm{~kg} / \mathrm{m}^{3}$
(D) $250 \mathrm{~kg} / \mathrm{m}^{3}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
03:20

Problem 6

Two blocks $A$ and $B$ made of iron and aluminium, respectively, have exactly the same weight. They are completely immersed in water and weighed. If the densities of iron and aluminium are $8000 \mathrm{~kg} / \mathrm{m}^{3}$ and $2700 \mathrm{~kg} / \mathrm{m}^{3}$, then
(A) $A$ will weigh more than $B$
(B) $B$ will weigh more than $A$
(C) $A$ and $B$ will weigh the same as before
(D) Data insufficient

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:20

Problem 7

A body of mass $0.5 \mathrm{~kg}$ is attached to a thread and it just floats in a liquid. The tension in the thread is
(A) $0.5 \mathrm{~kg} \mathrm{wt}$
(B) More than $0.5 \mathrm{~kg}$ wt
(C) Less than $0.5 \mathrm{~kg} \mathrm{wt}$
(D) Zero

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:39

Problem 8

Equal volumes of water and alcohol are mixed together. The density of water is $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and the density of alcohol is $800 \mathrm{~kg} / \mathrm{m}^{3}$. The density of the mixture is
(A) $900 \mathrm{~kg} / \mathrm{m}^{3}$
(B) $1100 \mathrm{~kg} / \mathrm{m}^{3}$
(C) $875 \mathrm{~kg} / \mathrm{m}^{3}$
(D) $950 \mathrm{~kg} / \mathrm{m}^{3}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:44

Problem 9

A water tank is $20 \mathrm{~m}$ deep. If the water barometer reads $10 \mathrm{~m}$, the pressure at the bottom of the tank is
(A) 2 atmosphere
(B) 1 atmosphere
(C) 3 atmosphere
(D) 4 atmosphere

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:50

Problem 10

The three vessels shown in Fig. $8.33(\mathrm{~A}-\mathrm{C})$ have exactly the same base area. Equal volumes of a liquid are poured in the three vessels. The force on the base will be
(A) Maximum in vessel $\mathrm{A}$
(B) Maximum in vessel $\mathrm{B}$
(C) Maximum in vessel $\mathrm{C}$
(D) Equal in all the vessels

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:37

Problem 11

An incompressible, non-viscous fluid flows steadily through a cylindrical pipe, which has radius $2 R$ at point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity of flow at point $A$ is $v$, the velocity of flow at point $B$ will be
(A) $2 v$
(B) $v$
(C) $v / 2$
(D) $4 \mathrm{v}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:02

Problem 12

A barometer kept in an elevator accelerating upward reads $76 \mathrm{~cm}$. The air pressure in the elevator is
(A) $76 \mathrm{~cm}$
(B) $<76 \mathrm{~cm}$
(C) $>76 \mathrm{~cm}$
(D) Zero

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:10

Problem 13

To get the maximum flight, a ball must be thrown as(A)(C)(B)(D) Any of $(\mathrm{A}),(\mathrm{B})$, and $(\mathrm{C})$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:51

Problem 14

The weight of a body in water is one-third of its weight in air. The density of the body is
(A) $0.5 \mathrm{gm} / \mathrm{cm}^{3}$
(B) $1.5 \mathrm{gm} / \mathrm{cm}^{3}$
(C) $2.5 \mathrm{gm} / \mathrm{cm}^{3}$
(D) $3.5 \mathrm{gm} / \mathrm{cm}^{3}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:02

Problem 15

The volume of a liquid flowing per sec out of an orifice at the bottom of a tank does not depend upon
(A) the height of the liquid above the orifice.
(B) the acceleration due to gravity.
(C) the density of the liquid.
(D) the area of the orifice.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:55

Problem 16

One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof, and a weight $W_{1}$ is suspended from its lower end. If $S$ is the area of cross-section of the wire, the stress in the wire at a height ( $3 L / 4$ ) from its lower end is
(A) $W_{1} / S$
(B) $\left[W_{1}+(W / 4)\right] / S$
(C) $\left[W_{1}+(3 W / 4)\right] / S$
(D) $\left[W_{1}+W\right] / S$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:33

Problem 17

A wire can sustain the weight of $20 \mathrm{~kg}$ before breaking. If the wire is cut into two equal parts, each part can sustain a weight of
(A) $10 \mathrm{~kg}$
(B) $20 \mathrm{~kg}$
(C) $40 \mathrm{~kg}$
(D) $80 \mathrm{~kg}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:41

Problem 18

A solid uniform ball having volume $V$ and density $\rho$ floats at the interface of two immiscible liquids as shown in Fig. $8.34$. The densities of the upper and the lower liquids are $\rho_{1}$ and $\rho_{2}$, respectively, such that $\rho_{1}<$ $\rho<\rho_{2}$. The fraction of the volume of the ball in the lower liquid is
(A) $\frac{\rho-\rho_{2}}{\rho_{1}-\rho_{2}}$
(B) $\frac{\rho_{1}}{\rho_{1}-\rho_{2}}$
(C) $\frac{\rho_{1}-\rho}{\rho_{1}-\rho_{2}}$
(D) $\frac{\rho_{1}-\rho_{2}}{\rho_{2}}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:56

Problem 19

The deformation of a wire under its own weight compared to the deformation of same wire subjected to a load equal to the weight of the wire is
(A) Same
(B) One-third
(C) Half
(D) One-fourth

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:10

Problem 20

The weight of a body in air is $100 \mathrm{~N}$. Its weight in water, if it displaces $400 \mathrm{cc}$ of water is
(A) $90 \mathrm{~N}$
(B) $94 \mathrm{~N}$
(C) $98 \mathrm{~N}$
(D) None of these

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
03:05

Problem 21

The specific gravity of ice is $0.9$. The area of the smallest slab of ice of height $0.5 \mathrm{~m}$ floating in fresh water that will just support a $100 \mathrm{~kg}$ man is
(A) $1.5 \mathrm{~m}^{2}$
(B) $2 \mathrm{~m}^{2}$
(C) $3 \mathrm{~m}^{2}$
(D) $4 \mathrm{~m}^{2}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:50

Problem 22

A liquid stands at the same level in the U-tube when at rest. If area of cross-section of both the limbs are equal, the difference in heights $h$ of the liquid in thetwo limbs of $U$-tube, when the system is given an acceleration $a$ in horizontal direction as shown, is
(A) $\frac{g L^{2}}{a H}$
(B) $\frac{L a}{g}$
(C) $\frac{L^{2} a}{H g}$
(D) $\frac{H g}{a}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:25

Problem 23

Figure $8.35$ shows a semi-cylindrical massless gate (of width $R$ ) pivoted at the point $O$ holding a stationary liquid of density $\rho .$ A horizontal force $F$ is applied at its lowest position to keep it stationary. The magnitude of the force is
Fig. $8.35$
(A) $\frac{9}{2} \rho g R^{3}$
(B) $\frac{3}{2} \rho g R^{3}$
(C) $\rho g R^{3}$
(D) Zero

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:23

Problem 24

A block $A$ of mass $10 \mathrm{~kg}$, connected to another hollow block $B$ of same size and negligible mass, by a spring of spring constant $500 \mathrm{~N} / \mathrm{m}$, floats in water as shown in Fig. 8.36. The compression in the spring is $\left(\rho_{\text {water }}=1 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}, g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $10 \mathrm{~cm}$
(B) $20 \mathrm{~cm}$
(C) $50 \mathrm{~cm}$
(D) $100 \mathrm{~cm}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
03:29

Problem 25

A conical block floats in water with $90 \%$ height immersed in it. Height $h$ of the block is equal to the diameter of the block, i.e., $20 \mathrm{~cm}$. The mass to be kept on the block, so that the block just floats at the surface of water, is
(A) $568 \mathrm{~g}$
(B) $980 \mathrm{~g}$
(C) $112 \mathrm{~g}$
(D) $196 \mathrm{~g}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:57

Problem 26

A large cylindrical tank has a hole of area $A$ at its bottom. Water is poured in the tank by a tube of equal cross-sectional area $A$ ejecting water at the speed $v$.
(A) The water level in the tank will keep on rising.
(B) No water can be stored in the tank.
(C) The water level will rise to a height $v^{2} / 2 g$ and then stop.
(D) The water level will oscillate.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:46

Problem 27

A tank is filled with water and an orifice is made in the wall so that the horizontal range $x$ of water rushing out is maximum. If $H$ is the height of water above the orifice in the tank, then
(A) $x=H$
(B) $x=2 H$
(C) $2 x=H$
(D) $4 x=H$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:08

Problem 28

There is a small hole at the bottom of a large open vessel. If water is filled up to a height $h$, velocity of water coming out of hole is $v$. Then velocity of water coming out of hole when water is filled to a height $4 h$ is
(A) $4 v$
(B) $3 v$
(C) $2 \mathrm{v}$
(D) $y$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:49

Problem 29

A gas having density $\rho$ flows with a velocity $v$ along a pipe of cross-sectional area $s$ and bent at an angle of $90^{\circ}$ at a point $A$. The force exerted by the gas on the pipe at $A$ is
(A) $\frac{\sqrt{2} s v}{\rho}$
(B) $s v^{2} \rho$
(C) $\frac{\sqrt{3} s v^{2} \rho}{2}$
(D) $s v^{2} \rho$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:32

Problem 30

Water flows through a frictionless duct with a cross-section varying as shown in Fig. 8.37. Pressure $p$ at points along the axis is represented by
(A)
(B)
(C)
(D)

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:06

Problem 31

The dimensional formula for coefficient of viscosity
(A) $\left[\mathrm{MLT}^{-1}\right]$
(B) $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]$
(C) $\left[\mathrm{MLT}^{-2}\right]$
(D) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:03

Problem 32

Which of the following has greatest viscosity?
(A) Hydrogen
(B) Air
(C) Water
(D) Ammonia

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:05

Problem 33

With increase in temperature, the viscosity of
(A) both gases and liquids increases.
(B) both gases and liquids decreases.
(C) gases increases and of liquids decreases.
(D) gases deceases and of liquids increases.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:34

Problem 34

The profile of advancing liquid in a tube is a
(A) Straight line
(B) Circle
(C) Parabola
(D) Hyperbola

Mahendra K
Mahendra K
Numerade Educator
01:03

Problem 35

Terminal velocity of water drops depends upon the
(A) Radius of drop
(B) Charge of drop
(C) Temperature of drop
(D) Velocity of light

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:58

Problem 36

Water rises in a vertical capillary tube up to a length of $10 \mathrm{~cm}$. If the tube is inclined at $45^{\circ}$, the length of water arisen in the tube will be
(A) $10 \sqrt{2} \mathrm{~cm}$
(B) $10 \mathrm{~cm}$
(C) $10 / \sqrt{2} \mathrm{~cm}$
(D) None of these

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:03

Problem 37

The surface tension of a liquid is $5 \mathrm{~N} / \mathrm{m}$. If a film is held on a ring of area $0.02 \mathrm{~m}^{2}$, its total surface energy is about
(A) $5 \times 10^{-2} \mathrm{~J}$
(B) $2.5 \times 10^{-2} \mathrm{~J}$
(C) $2 \times 10^{-1} \mathrm{~J}$
(D) $3 \times 10^{-1} \mathrm{~J}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:38

Problem 38

If the angle of contact is $0^{\circ}$, the shape of meniscus is
(A) Plane
(B) Parabolic
(C) Cylindrical
(D) Hemispherical

Vysakh M
Vysakh M
Numerade Educator
02:02

Problem 39

The pressure just below the meniscus of water
(A) is greater than just above it.
(B) is lesser than just above it.
(C) is same as just above it.
(D) is always equal to atmospheric pressure.

Vysakh M
Vysakh M
Numerade Educator
01:26

Problem 40

A soap bubble is blown slowly at the end of a tube by
a pump supplying air at a constant rate. Which one of the following graphs represents the correct variation of the excess of pressure inside the bubble with time?
(A)
(B)
(C)
(D)

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:07

Problem 41

The viscous force on a small sphere of radius $R$ moving in a fluid varies as
$(\mathrm{A}) \propto R^{2}$
(B) $\propto R$
(C) $\propto(1 / R)$
$(\mathrm{D}) \propto(1 / R)^{2}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:23

Problem 42

If a small sphere is let to fall vertically in a large quantity of a still liquid of density smaller than that of the material of the sphere
(A) At first its velocity increases, but soon approaches a constant value.
(B) It falls with constant velocity all along from the very beginning.
(C) At first it falls with a constant velocity which after some time goes on decreasing.
(D) Nothing can be said about its motion.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:41

Problem 43

A small spherical solid ball is dropped in a viscous liquid. Its journey in the liquid is best described in Fig. $8.38$ drawn by
(A) Curve $A$
(B) Curve $B$
(C) Curve $C$
(D) Curve $D$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:15

Problem 44

Rain drops fall from a height under gravity, we observe that
(A) Their velocities go on increasing until they hit the ground but the velocity with which the drops hit the ground differs with the radius of the rain drop.
(B) Their velocities go on increasing until they hit the ground, velocity being independent of the radius of the drop.
(C) They fall with a terminal velocity which is dependent of the radius of the rain drop.
(D) They fall with a terminal velocity which depends upon the radius of the rain drop.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:14

Problem 45

Air is pushed into a soap bubble of radius $r$ to double its radius. If the surface tension of the soap solution is $S$, the work done in the process is
(A) $8 \pi r^{2} S$
(B) $12 \pi r^{2} S$
(C) $16 \pi r^{2} S$
(D) $24 \pi r^{2} S$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:27

Problem 46

Water flows in a continuous stream down a vertical pipe, whereas it breaks into drops when falling freely because of(A) Viscosity
(B) Surface tension
(C) Atmospheric pressure
(D) Hydrostatic pressure

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:15

Problem 47

A soap bubble (surface tension 30 dyne/cm) has a radius of $2 \mathrm{~cm}$. The work done in doubling its radius is
(A) Zero
(B) $2261 \mathrm{erg}$
(C) $1135.5 \mathrm{erg}$
(D) 9043 erg

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:17

Problem 48

An air bubble of radius $r$ in water is at a depth $h$ below the water surface at some instant. If $P$ is atmospheric pressure and $d$ and $T$ are the density and surface tension of water, respectively, the pressure inside the bubble will be
(A) $P+h d g-\frac{4 T}{r}$
(B) $P+h d g+\frac{2 T}{r}$
(C) $P+h d g-\frac{2 T}{r}$
(D) $P+h d g+\frac{4 T}{r}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:24

Problem 49

Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by $75 \times 10^{-4} \mathrm{~N}$, force due to the weight of the liquid. If the surface tension of water is $6 \times 10^{-2} \mathrm{~N} / \mathrm{m}$, the inner circumference of the capillary must be
(A) $1.25 \times 10^{-2} \mathrm{~m}$
(B) $0.50 \times 10^{-2} \mathrm{~m}$
(C) $6.5 \times 10^{-2} \mathrm{~m}$
(D) $12.5 \times 10^{-2} \mathrm{~m}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:26

Problem 50

In a surface tension experiment with a capillary tube, water rises up to $0.1 \mathrm{~m}$. If the same experiment is repeated on an artificial satellite, which is revolving around the earth, water will rise in the capillary tube up to a height of
(A) $0.1 \mathrm{~m}$
(B) $0.2 \mathrm{~m}$
(C) $0.98 \mathrm{~m}$
(D) Full length of tube

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:31

Problem 51

A mercury barometer reads $75 \mathrm{~cm}$. If the tube be inclined by $60^{\circ}$ from vertical, the length of mercury in the tube will be
(A) $37.5 \mathrm{~cm}$
(B) $150 \mathrm{~cm}$
(C) $\frac{75 \sqrt{3}}{2} \mathrm{~cm}$
(D) $100 \mathrm{~cm}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:10

Problem 52

Two circular metal plates of radius $1 \mathrm{~m}$ and $2 \mathrm{~m}$ are placed horizontally in a liquid at rest at the same depth. The ratio of thrusts on them is
(A) $1: 2$
(B) $1: 1$
(C) $1: 4$
(D) $4: 1$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:02

Problem 53

A ball of mass $m$ and radius $r$ is released in viscous liquid. The value of its terminal velocity is proportional to
(A) $(1 / r)$ only
(B) $\mathrm{m} / \mathrm{r}$
(C) $(m / r)^{1 / 2}$
(D) $m$ only

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:35

Problem 54

Two capillary tubes of same length $l$ but radii $r_{1}$ and $r_{2}$ are fitted in parallel to the bottom of a vessel. The pressure head is $P .$ What should be the radius $r$ of the single tube that can replace the two tubes, so that the rate of flow is same as before?
(A) $r=r_{1}+r_{2}$
(B) $r=r_{1}^{2}+r_{2}^{2}$
(C) $r^{4}=r_{1}^{4}+r_{2}^{4}$
(D) $\frac{1}{r}=\frac{1}{r_{1}}+\frac{1}{r_{2}}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:30

Problem 55

If two soap bubbles of radii $r_{1}$ and $r_{2}\left(>r_{1}\right)$ are in contact, the radius of their common interface is
(A) $r_{1}+r_{2}$
(B) $\left(r_{1}+r_{2}\right)^{2}$
(C) $\frac{r_{1} r_{2}}{r_{2}-r_{1}}$
(D) $\sqrt{r_{1} r_{2}}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:10

Problem 56

On putting a capillary tube in a pot filled with water, the level of water rises up to a height of $4 \mathrm{~cm}$ in the tube. If a tube of half the diameter is used, the water will rise to the height of nearly
(A) $2 \mathrm{~cm}$
(B) $5 \mathrm{~cm}$
(C) $8 \mathrm{~cm}$
(D) $11 \mathrm{~cm}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:41

Problem 57

A small spherical solid ball is dropped in a viscous liquid. Its journey in the liquid is best described in Fig. 8.39 drawn by
(A) Curve $A$
(B) Curve $B$
(C) Curve $C$
(D) Curve $D$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:13

Problem 58

A boat with wood is floating in a lake. If the wood is thrown in the lake, the water level will
(A) Go up
(B) Go down
(C) Remain unchanged
(D) None of the above

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:12

Problem 59

The amount of work done in increasing the size of a soap film $10 \mathrm{~cm} \times 6 \mathrm{~cm}$ to $10 \mathrm{~cm} \times 10 \mathrm{~cm}$ is (S.T. =
$\left.30 \times 10^{-3} \mathrm{~N} / \mathrm{m}\right)$
(A) $2.4 \times 10^{-2} \mathrm{~J}$
(B) $1.2 \times 10^{-2} \mathrm{~J}$
(C) $2.4 \times 10^{-4} \mathrm{~J}$
(D) $1.2 \times 10^{-4} \mathrm{~J}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:55

Problem 60

One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight $W_{1}$ is suspended from its lower end. If $S$ is the area of cross-section of the wire, the stress in the wire at height ( $3 L / 4$ ) from its lower end is

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:07

Problem 61

If Young's modulus of iron is $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ and the interatomic spacing between two molecules is $3 \times 10^{-10} \mathrm{~m}$, the interatomic force constant is
(A) $60 \mathrm{~N} / \mathrm{m}$
(B) $120 \mathrm{~N} / \mathrm{m}$
(C) $3 \mathrm{~N} / \mathrm{m}$
(D) $180 \mathrm{~N} / \mathrm{m}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:36

Problem 62

Two rods of identical dimensions, with Young's modulus $Y_{1}$ and $Y_{2}$ are joined end to end. The equivalent Young's modulus for the composite rod is
(A) $\frac{2 Y_{1} Y_{2}}{Y_{1}+Y_{2}}$
(B) $\frac{Y_{1} Y_{2}}{Y_{1}+Y_{2}}$
(C) $\frac{1}{2\left(Y_{1}+Y_{2}\right)}$
(D) $Y_{1}+Y_{2}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:53

Problem 63

A uniform rod of length $L$ has a mass per unit length $\lambda$ and area of cross-section $A .$ The elongation in the rod is $l$ due to its own weight if it is suspended from the ceiling of a room. The Young's modulus of the rod is
(A) $\frac{2 \lambda g L^{2}}{A l}$
(B) $\frac{\lambda g L^{2}}{2 A l}$
(C) $\frac{2 \lambda g L}{A l}$
(D) $\frac{\lambda g l^{2}}{A L}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:18

Problem 64

If $A$ denotes the area of free surface of a liquid and $\bar{h}$ the depth of an orifice of area of cross-section $a$, below the liquid surface, then the velocity $v$ of flow through the orifice is given by
(A) $v=\sqrt{(2 g h)}$
(B) $v=\sqrt{(2 g h)} \sqrt{\left(\frac{A^{2}}{A^{2}-a^{2}}\right)}$
(C) $v=\sqrt{2 g h} \sqrt{\left(\frac{A}{A-a}\right)}$
(D) $v=\sqrt{2 g h} \sqrt{\left(\frac{A^{2}-a^{2}}{A^{2}}\right)}$

Mahendra K
Mahendra K
Numerade Educator
01:56

Problem 65

A wire of length $L$ and cross-sectional area $A$ is made of a material of Young's modulus $Y .$ If the wire is stretched by an amount $x$, the work done is
(A) $\frac{Y A x^{2}}{2 L}$
(B) $\frac{Y A x}{2 L^{2}}$
(C) $\frac{Y A x}{2 L}$
(D) $\frac{Y A x^{2}}{L}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:14

Problem 66

For the arrangement shown in Fig. $8.40$, the force at the bottom of the vessel is(A) $200 \mathrm{~N}$
(B) $100 \mathrm{~N}$
(C) $20 \mathrm{~N}$
(D) $2 \mathrm{~N}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:09

Problem 67

A cylindrical vessel of $90 \mathrm{~cm}$ height is kept filled up to its brim. It has four holes $1,2,3,4$ which are, respectively, at heights of $20 \mathrm{~cm}, 30 \mathrm{~cm}, 45 \mathrm{~cm}$, and $50 \mathrm{~cm}$ from the horizontal floor $P Q$. The water falling at the maximum horizontal distance from the vessel comes from
(A) Hole number 4
(B) Hole number 3
(C) Hole number 2
(D) Hole number 1

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:08

Problem 68

An open vessel containing water is given a constant acceleration $a$ in the horizontal direction. Then the free surface of water gets sloped with the horizontal at an angle $\theta$ given by
(A) $\theta=\tan ^{-1}\left(\frac{a}{g}\right)$
(B) $\theta=\tan ^{-1}\left(\frac{g}{a}\right)$
(C) $\theta=\sin ^{-1}\left(\frac{a}{g}\right)$
(D) $\theta=\cos ^{-1}\left(\frac{g}{a}\right)$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
00:51

Problem 69

The stress-strain graph for two materials is shown in Fig. $8.41$. If the Young's modulus for two materials are $Y_{A}$ and $Y_{B}$ then
Fig. $8.41$
(A) $Y_{A}=Y_{B}$
(B) $Y_{A}>Y_{B}$
(C) $Y_{A}<Y_{B}$
(D) Can't be predicted from the graph

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:52

Problem 70

A metal wire of length $L$, area of cross-section $\mathrm{A}$, and Young's modulus $Y$ is stretched by a variable force $F$ such that $F$ is always slightly greater than the elastic forces of resistance in the wire. When the elongation of the wire is $\ell$
(A) The work done by $F$ is $\frac{Y A \ell^{2}}{2 L}$
(B) The work done by $F$ is $\frac{Y A \ell^{2}}{L}$
(C) The elastic potential energy stored in the wire is $\frac{Y A \ell^{2}}{2 L}$
(D) No heat is produced during the elongation

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:20

Problem 71

A large wooden plate of area $10 \mathrm{~m}^{2}$ floating on the surface of a river is made to move horizontally with a speed of $2 \mathrm{~m} / \mathrm{s}$ by applying a tangential force. River is $1 \mathrm{~m}$ deep and the water in contact with the bed is stationary. Then choose the correct statements. (Coefficient of viscosity of water $\left.=10^{-3} \mathrm{Ns} / \mathrm{m}^{2}\right)$(A) Velocity gradient is $2 \mathrm{~s}^{-1}$.
(B) Velocity gradient is $1 \mathrm{~s}^{-1}$.
(C) Force required to keep the plate moving with constant speed is $0.02 \mathrm{~N}$.
(D) Force required to keep the plate moving with constant speed is $0.01 \mathrm{~N}$.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:34

Problem 72

A tank, which is open at the top, contains a liquid up to a height $H$. A small hole is made in the side of the tank at a distance $y$ below the liquid surface. The liquid emerging from the hole lands at a distance $x$ from the $\operatorname{tank}$
(A) If $y$ is increased from zero to $H, x$ will first increase and then decrease.
(B) $x$ is maximum for $y=H / 2$.
(C) The maximum value of $x$ is $H$.
(D) The maximum value of $x$ will depend on the density of the liquid.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:38

Problem 73

An object is floating in a liquid, kept in a container. The container is placed in a lift. Choose the correct option(s).
(A) Buoyant force increases as lift accelerates up.
(B) Buoyant force decreases as lift accelerates up.
(C) Buoyant force remains constant as lift accelerates.
(D) The fraction of solid submerged into liquid does not change.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
03:09

Problem 74

A small solid ball of density $\rho$ is held inside at point
$A$. A cubical container of side $L$, filled with an ideal liquid of density $4 \rho$ as shown in Fig. $8.42$. Now, if the container starts moving with constant acceleration
a horizontally and the ball is released from point $A$ simultaneously, then
Fig. $8.42$(A) For ball to hit the top of container at end $Q$, $a=3 \mathrm{~g}$.
(B) For ball to hit the top of container at end $Q$, $a=2 \mathrm{~g}$.
(C) Ball hits the top of container at end $Q$ after a time $t=\sqrt{\frac{L}{3 g}}$.
(D) Ball hits the top of container at end $Q$ after a time $t=\sqrt{\frac{2 L}{3 g}}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:39

Problem 75

A block of mass $m$ is attached by means of a spring to the bottom of a tank of water as shown in Fig. $8.43$. At equilibrium, the spring is under compression. If the tank is now allowed to fall freely, then choose the correct alternative(s).
(A) The spring comes to its relaxed position.
(B) The spring compresses more than its equilibrium compression.
(C) The buoyant force becomes zero.
(D) There will be some elongation is the spring.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
04:12

Problem 76

What is the value of $a ?$
(A) $2 m g$
(B) $m g$
(C) $\frac{m g}{2}$
(D) $\frac{m g}{4}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
04:12

Problem 77

What is the value of $b ?$
(A) 1
(B) 2
(C) 3
(D) 4

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:09

Problem 78

If tension in the string at $x=4 h$ is $T_{1}$ and $T_{2}$ at $x=h$ then $T_{1} / T_{2}$ is
(A) 2
(B) 1
(C) $1 / 2$
(D) $1 / 4$Passage 2 A heavy rod of length $\ell$ is released from a height $h$ above the water surface as shown in Fig. $8.45 .$ The rod falls in air and then in water such that it always remains in vertical position. Neglecting the viscous force and drag force on rod while moving in air and water. Also the relative density of the rod is 2 neglecting the loss in energy when rod hitsthe surface. Assuming the water level remains unchanged due to fall of the rod and it touches the bottom of the tank at same speed. The cross-sectional area of the rod is $A$ and is constant. $\rho_{w}=$ density of water

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:42

Problem 79

The average body and force until rod sinks completely
(A) $2 \rho_{w} \lg A$
(B) $\frac{\rho_{w} \lg A}{2}$
(C) $\rho_{w} \lg A$
(D) $\frac{\rho_{w} l A g}{3}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:27

Problem 80

The work done by rod against buoyant fore until rod sinks completely
(A) $\rho_{w} A l^{2} g$
(B) $\frac{\rho_{w} A l^{2} g}{2}$
(C) $2 \rho_{w} A l^{2} g$
(D) Zero

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:06

Problem 81

Buoyant force varies as the displacement of the rod is best represented by
(A)
(B)
(C)
(D)Passage 3 A wire is bend at an angle $\theta . \mathrm{A}$ rod of mass $m$ can slide along the bend wire without friction as shown in Fig. $8.46$. If a soap film is maintained in the frame and frame is kept in a vertical position, the rod is in equilibrium.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:49

Problem 82

Surface tension of the soap solution is
(A) $\frac{m g}{4 \ell \tan \frac{\theta}{2}}$
(B) $\frac{m g}{2 \ell \tan \frac{\theta}{2}}$
(C) $\frac{m g}{4 \ell \tan \theta}$
(D) None of these

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:54

Problem 83

If rod is displaced slightly in vertical direction, then
(A) Motion is periodic but not SHM.
(B) Motion is periodic and SHM.
(C) The rod always moves vertically downward.
(D) None of these.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:04

Problem 84

If rod is displaced slightly in vertical direction, find the time period of small oscillation.
(A) $\pi \sqrt{\frac{l}{g}}$
(B) $2 \pi \sqrt{\frac{l}{g}}$
(C) $\frac{\pi}{2} \sqrt{\frac{l}{g}}$
(D) None of thesePassage 4 Figure $8.47$ shows a container having ideal liquid of variable density. The density of liquid varies as $\rho=\rho_{0}\left(4-\frac{3 h}{h_{0}}\right)$, where $h_{0}$ is height of liquid in container, $\rho_{0}$ is constant and $h$ is height from bottom. A solid block of small dimensions whose density $\frac{5}{2} \rho_{0}$ and mass $m$ is released from bottom of tank.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
05:16

Problem 85

The motion of the block is
(A) Periodic but not SHM.
(B) SHM.
(C) Oscillatory but not SHM.
(D) Oscillatory but not periodic.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
05:16

Problem 86

After what time does the block reach its initial position?
(A) $2 \pi \sqrt{\frac{5 h_{0}}{6 g}}$
(B) $2 \pi \sqrt{\frac{h_{0}}{g}}$
(C) $\pi \sqrt{\frac{h_{0}}{3 g}}$
(D) $\pi \sqrt{\frac{5 h_{0}}{6 g}}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
05:16

Problem 87

Maximum speed of block is
(A) $\sqrt{\frac{g h_{0}}{5}}$
(B) $\sqrt{2 g h_{0}}$
(C) $\sqrt{\frac{3 g h_{0}}{10}}$
(D) $\sqrt{\frac{10}{3} g h_{0}}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
05:16

Problem 88

Maximum height reached by the block
(A) $\frac{h_{0}}{2}$
(B) $h_{0}$
(C) $\frac{3 h_{0}}{4}$
(D) $\frac{h_{0}}{4}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:23

Problem 89

Assuming that all the liquid drop or a?r bubble have surface tension $T$ and radius $R$Column-I Column-II
(A) Excess pressure of liquid
(1) $\frac{4 T}{R}+\rho g h$
drop in air is
(B) Excess pressure of bubble in
(2) $\frac{2 T}{R}+\rho g h$
air is
(C) Excess pressure of air bubble
(3) $\frac{4 T}{R}$
in liquid at its free surface is
(D) Excess pressure of air bubble
(4) $2 \frac{T}{R}$.
in liquid at depth $\mathrm{h}$ from free surface is

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:39

Problem 90

A rectangular block of density $\rho$, base area $A$, and height $h$ is kept on a spring. The lower end of spring is fixed on the bottom of an empty vessel of base area $2 A$. The block compresses the spring by $h / 4$ at equilibrium. The vessel is then slowly filled by a liquid of density$2 \rho$ till the spring becomes relaxed. The block is then slowly pushed inside the liquid till it is immersed completely. Work done to push the block completely inside is $W_{1}$, work done by gravity on the block is $W_{2}$, and work done by upthrust is $W_{3}$. Match the following based on the above statements.\begin{tabular}{l}
Column-I \\
\hline (A) $\left|W_{1}\right|$
\end{tabular} Column-II
(1) $\frac{5 \rho g h^{2} A}{8}$
1 $\frac{\rho g h^{2} A}{8}$ $\left|W_{2}\right|$
(B)
(2)
0 (C) $\frac{3 \rho g h^{2} A}{4}$ $\left|W_{3}\right|$
(3)
(4) $\frac{\rho g h^{2} A}{4}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:46

Problem 91

Assertion: In case of motion of an ideal fluid in a horizontal tube, where the area of cross-section is minimum, pressure is maximum. Reason: Hydrostatic pressure in different ideal liquids at points of different depth can be same.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:27

Problem 92

Assertion: Force of buoyancy due to atmosphere on a body is almost zero (or negligible). Reason: The body is completely submerged in the atmosphere.
(A) $\mathrm{A}$
(B) B
(C) $\mathrm{C}$
(D) D

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:45

Problem 93

Assertion:
to elastic limit of a stress-strain curve the steel wire tends to regain its original shape when stress is removed.Reason: Within elastic limit the wire follows Hook's law.
(A) A
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:03

Problem 94

Assertion: When an ideal fluid flows through a horizontal tube of variable cross-section, the pressure becomes different at different points. Reason: Raindrops falling from a great height reach the ground with a relatively small velocity. This phenomenon involves the viscosity of air.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:45

Problem 95

A structural steel rod has a radius of $10 \mathrm{~mm}$ and a length of $1 \mathrm{~m}$. A $100 \mathrm{kN}$ force $F$ stretches it along its length. The strain in rod is $1.59 \times 10^{-n}$ then the value of $\mathrm{n}$ is. Given that the Young's modulus $E$ of the structural steel is $2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^{-2}$.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
00:42

Problem 96

A hollow conical vessel floats in water with its vertex downwards with a certain depth of its axis immersed. When water is poured into it up to the level originally immersed, it sinks till its mouth is on level with the surface of water. The fraction of its height that was originally under water is $\left(\frac{h}{H}\right)=\left(\frac{1}{2}\right)^{1 / n}$. Find the value of $n$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:34

Problem 97

A wooden plank of length $1 \mathrm{~m}$ and uniform cross-section is hinged at one end to the bottom of a tank as shown in Fig. $8.48$. The tank is filled with water up to a height of $0.5 \mathrm{~m}$. The specific gravity of the plank is $0.5$. The angle $\theta$ in radian that the plank makes with the vertical in the equilibrium position is $\frac{\pi}{n}$, then the value of $n$ is.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:17

Problem 98

A glass rod of diameter $d_{1}=1.5 \mathrm{~mm}$ is inserted symmetrically into a glass capillary of inside diameter $d_{2}=$ $2 \mathrm{~mm}$. Then the whole arrangement is vertically oriented and brought in contact with the surface of water. To what height (in $\mathrm{mm}$ ) will the water rise in the capillary (in $\mathrm{mm}$ )? (Density of water = $1 \mathrm{gm} / \mathrm{cc}$, surface tension $=0.07 \mathrm{~N} / \mathrm{m}$, angle of contact $=0^{\circ}, g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
05:56

Problem 99

Two opposite forces $F_{1}=120 \mathrm{~N}$ and $F_{2}=80 \mathrm{~N}$ act on an elastic plank of modulus of elasticity $Y=2 \times 10^{11}$ $\mathrm{N} / \mathrm{m}^{2}$ and length $\ell=1 \mathrm{~m}$ placed over a smooth horizontal surface. The cross-sectional area of the plank is $S=0.5 \mathrm{~m}^{2}$. The change in length of the plank is $x \times$ $10^{-11} \mathrm{~m}$, then find the value of $x$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:02

Problem 100

A U-tube having uniform cross-section but unequal arm lengths $\ell_{1}$ and $\ell_{2}\left(<\ell_{1}\right)$ has same liquid of density $\rho_{1}$ filled in it up to a height $h$ as shown in Fig. $8.49$. Another liquid of density $\rho_{2}=\left(\rho_{1} / 2\right)$ is poured in $\operatorname{arm} A$. Both liquids are immiscible. What length of the second liquid should be poured in $A$ so that first overtone of $A$ is in unison with fundamental tone of B? (Take $\ell_{1}=5 \mathrm{~m}, \ell_{2}=1 \mathrm{~m}$ and $h=0.5 \mathrm{~m}$ )

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:46

Problem 101

A piece of brass (Cu and $Z n$ ) weighs $12.9 \mathrm{~g}$ in air. When completely immersed in water, it weighs $11.3 \mathrm{~g}$. The relative densities of $\mathrm{Cu}$ and $\mathrm{Zn}$ are $8.9$ and $7.1$, respectively. Calculate the mass of copper in the alloy (in decigram).

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:01

Problem 102

A drop of water of mass $m=0.4 \mathrm{~g}$ is placed between two clean glass plates, the distance between which is $0.01 \mathrm{~cm}$. Find the force of attraction between the plates. Surface tension of water $=0.01 \mathrm{~N} / \mathrm{m}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:05

Problem 103

If $\mathrm{S}$ is stress and $Y$ is Young's modulus of material of a wire, the energy stored in the wire per unit volume is $[\mathbf{2 0 0 5}]$
(A) $2 S^{2} Y$
(B) $\frac{S^{2}}{2 Y}$
(C) $\frac{2 Y}{S^{2}}$
(D) $\frac{S}{2 Y}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:17

Problem 104

A wire is fixed at the upper end and stretches by length $\ell$ by applying a force $F .$ The work done in stretching is [2004](A) $\frac{F}{2 \ell}$
(B) $F \ell$
(C) $2 F \ell$
(D) $\frac{F \ell}{2}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:54

Problem 105

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200 \mathrm{~N}$ to the lower end. The weight stretches the wire by $1 \mathrm{~mm}$. Then, the elastic energy stored in the wire is $[2003]$
(A) $0.2 \mathrm{~J}$
(B) $10 \mathrm{~J}$
(C) $20 \mathrm{~J}$
(D) $0.1 \mathrm{~J}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:08

Problem 106

A wire elongates by $\ell m m$ when a load $\mathrm{w}$ is hung from it. If the wire goes over a pulley and two weights $w$ each are hung at the two ends, the elongation of the wire will be (in mm)
(A) $\ell$
(B) $2 \ell$
(C) Zero
(D) $\frac{\ell}{2}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:35

Problem 107

A spherical solid ball of volume $V$ is made of a material of density $\rho_{1}$. It is falling through a liquid of density $\rho_{2}\left(\rho_{2}<\rho_{1}\right.$ ) [Assuming that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $\left.F_{\text {viscous }}=-k v^{2}(k>0)\right]$. The terminal speed of the ball is [2008]
(A) $\sqrt{\frac{V g\left(\rho_{1}-\rho_{2}\right)}{k}}$
(B) $\frac{V g \rho_{1}}{k}$
(C) $\sqrt{\frac{V g \rho_{1}}{k}}$
(D) $\frac{V g\left(\rho_{1}-\rho_{2}\right)}{k}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:54

Problem 108

A jar is filled with two non-mixing liquids 1 and 2 having densities $\rho_{1}$ and $\rho_{2}$, respectively. A solid ball, made of a material of density $\rho_{3}$, is dropped in the jar. It comes to equilibrium in the position shown in Fig. 8.50. Which of the following is true for $\rho_{1}, \rho_{2}$ and $\rho_{3} ?$
$[2007]$
Fig. $8.50$
(A) $\rho_{3}<\rho_{1}<\rho_{2}$
(B) $\rho_{1}>\rho_{3}>\rho_{2}$
(C) $\rho_{1}>\rho_{2}>\rho_{3}$
(D) $\rho_{1}<\rho_{3}<\rho_{2}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:41

Problem 109

If the terminal speed of a sphere of gold (density = $19.5 \mathrm{kgm}^{-3}$ ) is $0.2 \mathrm{~ms}^{-1}$ in a viscous liquid (density $=$ $1.5 \mathrm{kgm}^{-3}$ ), find the terminal speed of a sphere of silver (density $=10.5 \mathrm{~kg} / \mathrm{m}^{-3}$ ) of the same size in the same liquid. [2006]
(A) $0.4 \mathrm{~ms}^{-1}$
(B) $0.133 \mathrm{~ms}^{-1}$
(C) $0.1 \mathrm{~ms}^{-1}$
(D) $0.2 \mathrm{~ms}^{-1}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:33

Problem 110

A $20 \mathrm{~cm}$ long capillary tube is dipped in water. The water rises up to $8 \mathrm{~cm}$. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
(A) $8 \mathrm{~cm}$
(B) $10 \mathrm{~cm}$
(C) $4 \mathrm{~cm}$
(D) $20 \mathrm{~cm}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:10

Problem 111

A spherical balls of a radius $R$ is falling in a viscous fluid of viscosity $\eta$ with a velocity $v .$ The retarding viscous force acting on the spherical ball is [2004]

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:47

Problem 112

If two soap bubbles of different radii are connected by a tube
(A) Air flows from the bigger bubble to the smaller bubble till the sizes become equal.
(B) Air flows from bigger bubble to the smaller bubble till the sizes are interchanged.
(C) Air flows from the smaller bubble to the bigger bubble.
(D) There is no flow of air.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:08

Problem 113

A cylinder of height $20 \mathrm{~m}$ is completely filled with water. The velocity of efflux of water (in $\mathrm{ms}^{-1}$ ) through a small hole on the side wall of the cylinder near its bottom is
(A) 10
(B) 20
(C) $25.5$
(D) 5

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:48

Problem 114

A uniform cylinder of length $\ell$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density at equilibrium position. The extension of the spring when it is in equilibrium is:
(A) $\frac{M g}{k}\left(1-\frac{\ell A \sigma}{M}\right)$
(B) $\frac{M g}{k}\left(1-\frac{\ell A \sigma}{2 M}\right)$
(C) $\frac{M g}{k}\left(1+\frac{\ell A \sigma}{M}\right)$
(D) $\frac{M g}{k}$

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
02:42

Problem 115

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is $T$, density of liquid is $\rho$, and $L$ is its latent heat of vaporization.
(A) $\sqrt{T / \rho L}$
(B) $T / \rho L$
(C) $2 T / \rho L$
(D) $\rho L / T$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:17

Problem 116

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_{1}$ and $d_{2}$ are filled in the tube. Each liquid subtends $90^{\circ}$ angle at the centre. Radius joining their interface makes an angle $\alpha$ with vertical plane. Ratio $\frac{d_{1}}{d_{2}}$ is [2014](A) $\frac{1+\sin \alpha}{1-\sin \alpha}$
(B) $\frac{1+\cos \alpha}{1-\cos \alpha}$
(C) $\frac{1+\tan \alpha}{1-\tan \alpha}$
(D) $\frac{1+\sin \alpha}{1-\cos \alpha}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:23

Problem 117

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius $R$ and making a circular contact of radius $r$ with the bottom of the vessel. If $r<<R$, and the surface tension of water is $T$, value of $r$ just before bubbles detach is
(Density of water is $\rho_{w}$ ) [2014](A) $R^{2} \sqrt{\frac{\rho_{w} g}{3 T}}$
(B) $R^{2} \sqrt{\frac{\rho_{w} g}{6 T}}$
(C) $R^{2} \sqrt{\frac{\rho_{w} g}{T}}$
(D) $R^{2} \sqrt{\frac{3 \rho_{w} g}{T}}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:18

Problem 118

A pendulum made of a uniform wire of cross-sectional area $A$ has time period $T$. When an additional mass $M$ is added to its bob, the time period changes to $T M$. If the Young's modulus of the material of the wire is $Y$, then $\frac{1}{Y}$ is equal to $(g=$ gravitational acceleration) $\quad[\mathbf{2 0 1 5}]$
(A) $\left[\left(\frac{T_{M}}{T}\right)^{2}-1\right] \frac{M g}{A}$
(B) $\left[1-\left(\frac{T_{M}}{T}\right)^{2}\right] \frac{A}{M g}$
(C) $\left[1-\left(\frac{T}{T_{M}}\right)^{2}\right] \frac{A}{M g}$
(D) $\left[\left(\frac{T_{M}}{T}\right)^{2}-1\right] \frac{A}{M g}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator