Arihant AIEEE Physics

D.B. Singh

Chapter 8

Rotation - all with Video Answers

Educators

+ 2 more educators

Chapter Questions

Problem 1

Mark correct option or options:
(a) Radial acceleration is equal to time derivative of radial velocity
(b) Radial acceleration is not equal to time derivative of radial velocity
(c) Transverse acceleration is time derivative of transverse velocity
(d) Both (b) and (c) are correct

Narayan Hari

Narayan Hari

Numerade Educator

Problem 2

A rigid body rotates with constant angular velocity $\omega$ about the line $x=\frac{y}{2}=\frac{z}{2}$, the speed of particle at the instant, it passes through the point $(2,3,5)$ is :
(a) $\omega$
(b) $2 \omega$
(c) $3 \omega$
(d) $\sqrt{2} \omega$

Dheeraj Sharma

Numerade Educator

Problem 3

The instantaneous velocity of point $B$ of the given rod of length $0.5$ metre is $3 \mathrm{~m} / \mathrm{s}$ in the represented direction. The angular velocity of the rod for minimum velocity of end $A$ is :
(a) $1.5 \mathrm{rad} / \mathrm{s}$
(b) $5.2 \mathrm{rad} / \mathrm{s}$
(c) $2.5 \mathrm{rad} / \mathrm{s}$
(d) none of these

Dheeraj Sharma

Numerade Educator

Problem 4

A car is moving in a circular horizontal track of radius $10 \mathrm{~m}$ with a constant speed of $10 \mathrm{~m} / \mathrm{sec}$. A plumb bob is suspended from the roof of the car by a light rigid rod of length $1 \mathrm{~m}$. The angle made by the rod with the track is: (Take $\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) zero
(b) $30^{\circ}$
(c) $45^{\circ}$
(d) $60^{\circ}$

Dheeraj Sharma

Numerade Educator

Problem 5

If a body completes a vertical circle, then
(a) total energy of body remains constant
(b) angular momentum remains constant
(c) angular velocity remains constant
(d) none of the above

Dheeraj Sharma

Numerade Educator

Problem 6

A block of mass $m$ having coefficient of friction $\mu$ with the floor $F$ is placed at one end of the spring. The spring is attached to this block and a vertical shafts. The floor with the shaft is given an angular acceleration $\alpha$. Then :(a) the spring cannot elongate before $t=\sqrt{\frac{\mu g}{l \alpha^{2}}}$
(b) the spring elongates as soon as the rotation starts
(c) the stored energy in the spring goes on increasing right from $t=0$ onwards
(d) the maximum spring force acts at $t=\sqrt{\frac{\mu g}{l \alpha^{2}}}$

Akshaya Rs

Numerade Educator

Problem 7

Moment of inertia of a copper sphere :
(a) depends upon temperature
(b) depends upon angular velocity
(c) depends upon the position of axis of rotation
(d) both (a) and (c) are correct

Dheeraj Sharma

Numerade Educator

Problem 8

Let $I_{A}$ and $I_{B}$ be moment of inertia of a body about two axis $A$ and $B$ respectively. The axis of body $A$ passes through the centre of mass of the body but $B$ does not. Then :
(a) $I_{A}<I_{B}$
(b) if $I_{A}<I_{B}$, the axes are parallel
(c) if the axes are parallel $I_{A}<I_{B}$
(d) if the axes are not parallel $I_{A}>I_{B}$

Dheeraj Sharma

Numerade Educator

Problem 9

An arc making $120^{\circ}$ at the centre of ring of mass $m$ and radius $r$ is cut from the ring. The arc is made to rotate about z-axis perpendicular to its plane and passing through the centre of the ring. The moment of inertia of the arc about the $z$ -axis:
(a) $m r^{2}$
(b) $\frac{m r^{2}}{3}$
(c) $\frac{m r^{2}}{2}$
(d) $\frac{m r^{2}}{4}$

Saman Zulfiqar

Numerade Educator

Problem 10

Mass of bigger disc having radius $2 R$ is $M$. A disc of radius $R$ is cut from bigger disc as shown in figure. Moment of inertia of disc about an axis passing through periphery and perpendicular to plane (shown in figure) is:
(a) $\frac{27 M R^{2}}{8}$
(b) $\frac{29 M R^{2}}{8}$
(c) $3.5 \mathrm{MR}$
(d) $2 M R^{2}$

Dheeraj Sharma

Numerade Educator

Problem 11

The ratio of the radii of gyration of a circular disc and a circular ring of the same radii about a tangential axis in the plane is :
(a) $1: 2$
(b) $\sqrt{5}: \sqrt{6}$
(c) $2: 3$
(d) $2: 1$

Dheeraj Sharma

Numerade Educator

Problem 12

The M.L. about an axis of symmetry is given by (mass x sum of square of perpendicular semi axes) $\times \frac{1}{n}$. Then:(a) if $n=3$, body is rectangular
(b) if $n=4$, body is elliptical
(c) if $n=5$, body is spherical
(d) all the above

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 13

The moment of inertia of a uniform solid right circular cone of mass $10 \mathrm{~kg}$, height $2 \mathrm{~m}$ and vertical angle $90^{\circ}$ about a diameter of its base, is:
(a) $10 \mathrm{kgm}^{2}$
(b) $20 \mathrm{kgm}^{2}$
(c) $30 \mathrm{kgm}^{2}$
(d) none of these

Vysakh M

Numerade Educator

Problem 14

Ram says, "A body may be in pure rotation in the presence of a single external force." Shyam says, "This is possible only for a non rigid body", then:
(a) Ram's statement is correct
(b) both statements are correct in different situations
(c) both statements are wrong
(d) both statements are stated by physicists

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 15

A particle of mass $m$ rotates in a circle of radius $a$ with a uniform angular speed $\omega_{0}$. It is viewed from a frame rotating about the $z$ -axis with a uniform angular speed
$\omega$. The centrifugal force on the particles is:
(a) $m \omega^{2} a$
(b) $m \omega_{0}^{2} a$
(c) $m\left(\frac{\omega+\omega_{0}}{2}\right)^{2} a$
(d) $m \omega \omega_{0}$

Dheeraj Sharma

Numerade Educator

Problem 16

The formula that torque equals the rate of change of angular momentum is true in following general cases:
(a) a fixed axis in inertial space
(b) an axis through the centre of mass even though the object may be accelerating
(c) a variable axis in inertial space
(d) both (a) and (c) are correct

Saman Zulfiqar

Numerade Educator

Problem 17

Mark correct option or options:
(a) The vector product of two polar vectors may be axial vector
(b) The vector product of two polar vectors must be axial vector
(c) The sense of direction of axial vector depends on the handedness of reference frame
(d) Both (b) and (c) are correct

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 18

If a raw egg and a boiled egg are spinned on the table by applying same torque, then:
(a) boiled egg will spin faster
(b) raw egg will spin faster
(c) moment of inertia of boiled egg will be lesser than that of the raw egg
(d) both (a) and (c) are correct

Dheeraj Sharma

Numerade Educator

Problem 19

The torque $\vec{\tau}$ on a body about a given point is found to be equal to $\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{L}}$ where $\overrightarrow{\mathrm{A}}$ is constant vector and $\overrightarrow{\mathbf{L}}$ is the angular momentum of the body about that point. From this it follows that :
(a) $\frac{\overrightarrow{3}}{\text { "i }}$ is perpendicular to $\overrightarrow{\mathbf{L}}$ at all instant of time
(b) the component of $\overrightarrow{\mathrm{L}}$ in the direction of $\overrightarrow{\mathrm{A}}$ does not change with time(c) the magnitude of $\overrightarrow{\mathbf{L}}$ does not change with time
(d) all the above

Saman Zulfiqar

Numerade Educator

Problem 20

Mark correct option or options:
(a) For neutral equilibrium, the potential energy is constant
(b) In stable equilibrium, potential energy is minimum
(c) For unstable equilibrium, potential energy is neither constant nor minimum
(d) All the above

Saman Zulfiqar

Numerade Educator

Problem 21

If a body is moving on a horizontal table with constant velocity, then equilibrium is:
(a) stable
(b) unstable
(c) neutral
(d) none of these

Saman Zulfiqar

Numerade Educator

Problem 22

A portmanteau of length $1.5 \mathrm{~m}$ and height $1 \mathrm{~m}$ is carried up stairs by two men, who hold it by the front and back edges of its lower face. If the portmanteau is inclined at $30^{\circ}$ to the horizontal and weighs $100 \mathrm{~kg}$, how much of the weight each man support?
(a) $6925 \mathrm{~N}$ and $30.75 \mathrm{~N}$
(b) $6.925 \mathrm{~N}$ and $3075 \mathrm{~N}$
(c) $500 \mathrm{~N}$ and $600 \mathrm{~N}$
(d) $400 \mathrm{~N}$ and $600 \mathrm{~N}$

Prem Bijarniya

Numerade Educator

Problem 23

The tricycle weighing $20 \mathrm{~kg}$ has a small wheel symmetrically placed $1 \mathrm{~m}$ behind the two large wheels, which are also $1 \mathrm{~m}$ apart. If the centre of gravity of machine be at a horizontal distance of $25 \mathrm{~cm}$ behind the front wheels and the rider whose weight is $40 \mathrm{~kg}$, be 10 $\mathrm{cm}$ behind the front wheels. The thrust on each front wheel is:
(a) $255 \mathrm{~N}$
(b) $90 \mathrm{~N}$
(c) $200 \mathrm{~N}$
(d) $400 \mathrm{~N}$

Dheeraj Sharma

Numerade Educator

Problem 24

Two halves of a round homogeneous cylinder are held together by a thread wrapped round the cylinder with two equal weights. The complete cylinder weighs $31.4 \mathrm{~kg}$. The plane of contact of both of its halves is vertical. For equilibrium of both halves of the cylinder, the minimum value of $m$ is :
(a) $\frac{2}{3} \mathrm{~g}$
(b) $3.14 \mathrm{~g}$
(c) $\frac{2}{3} \mathrm{~kg}$
(d) $31.4 \mathrm{~g}$

Saman Zulfiqar

Numerade Educator

Problem 25

A rod of length $L$ is pivoted at one end and is rotated with a uniform angular velocity in a horizontal plane. Let $T_{1}$ and $T_{2}$ be the tensions at the points $\frac{L}{4}$ and $\frac{3 L}{4}$ away from the pivoted end. Then:
(a) $T_{1}>T_{2}$
(b) $T_{2}>T_{1}$
(c) $T_{1}=T_{2}$
(d) the relation between $T_{1}$ and $T_{2}$ depends on whether the rod rotates clockwise or anti-clockwise

Dheeraj Sharma

Numerade Educator

Problem 26

A rectangular plate of mass $20 \mathrm{~kg}$ is suspended from points $A$ and $B$ as shown. If the pin $B$ is suddenly removed, determine the angular acceleration (in $\mathrm{rad} / \mathrm{sec}^{2}$ ) of the plate:(a) 48
(b) $19.6$
(c) $29.4$
(d) $23.6$

Dheeraj Sharma

Numerade Educator

Problem 27

A uniform rod of length $l$ and mas $m$ is suspended by two vertica inextensible string as shown figure. Then tension in the left strin when right string snaps, is :
(a) $\frac{3 m g}{4}$
(b) $\frac{m g}{4}$
(c) $\frac{m g}{2}$
(d) $\frac{m g}{8}$

Dheeraj Sharma

Numerade Educator

Problem 28

Two uniform equal ladders $A B$ and $A C$, each of weight $' w^{\prime}$ lean against each other and a string is tied between $B$ and $C$. They stand on a smooth horizontal surface. Then :
(a). the force exerted by one rod on the other at $A$ equal to the extension in the string
(b) tension $T=\left\{\frac{w}{2}\right) \cot \theta$
(c) the normal reaction at $B$ and $C$ are equal
(d) both (a) and (b) are correct

Dheeraj Sharma

Numerade Educator

Problem 29

In the given figure, the mass of blocks $A$ and $B$ are $m_{1}$ and $m_{2}$ respectively, the pulley is circular disc of mass $m$ and radius $r$. The pulley is free to rotate about $O$. No friction exists between $A$ and $B$ and the floor. The magnitude of acceleration of block $B$ is $a_{0}$. Then the magnitude of acceleration of $A$ is :
(a) $a_{0}$
(b) $2 a_{0}$
(c) $\sqrt{2} a_{0}$
(d) $g$

Dheeraj Sharma

Numerade Educator

Problem 30

A simple pendulum is vibrating with an angu amplitude of $90^{\circ}$ as shown in the figure. For what va of $\alpha$, the acceleration is directed horizontally?
(a) 0
(b) $90^{\circ}$
(c) $\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
(d) $\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)$

Saman Zulfiqar

Numerade Educator

Problem 31

A simple pendulum is vibrating with an angu amplitude of $90^{\circ}$ as shown in the figure. For what va of $\alpha$, the acceleration is directed horizontally?
(a) 0
(b) $90^{\circ}$
(c) $\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
(d) $\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)$

Saman Zulfiqar

Numerade Educator

Problem 32

A light rod carries three equal masses $A, B$ and $C$ as shown in figure. The velocity of $B$ in vertical position of rod if it is released from horizontal position as shown in figure is:
(a) $\sqrt{2 g} l$
(b) $\sqrt{\frac{18 g l}{7}}$
(c) $\sqrt{\frac{4 g l}{3}}$
(d) $\sqrt{\frac{8 g l}{7}}$

Dheeraj Sharma

Numerade Educator

Problem 33

The kinetic energy of a lamina moving in its plane is :
(a) $M\left(v_{\mathrm{cm}}^{\overline{ }}+\kappa^{2} \omega^{2}\right)$
(b) $\frac{1}{2} M\left(v_{\mathrm{cm}}^{2}+k^{2} \omega^{2}\right)$
(c) $\frac{1}{2} I \omega^{2}$
(d) none of these

Dheeraj Sharma

Numerade Educator

Problem 34

Mark correct option or options:
(a) The centre of gravity may be coincided with centre of mass
(b) Due to movement of body, centre of gravity changes but centre of mass does not change
(c) The centre of gravity must not be coincided with the centre of gravity
(d) The centre of gravity is always above the centre of mass

Saman Zulfiqar

Numerade Educator

Problem 35

At any instant, a rolling body may be considered to be in pure rotation about an axis through the point of contact. This axis is translating forward with speed:
(a) equal to centre of mass
(b) zero
(c) twice of centre of mass
(d) no sufficient data

Dheeraj Sharma

Numerade Educator

Problem 36

In the case of falling, rolling and sliding from same height :
(a) the falling body reaches bottom first and rolling at last
(b) the acceleration is maximum in falling and minimum in rolling
(c) the velocity of sliding is greater than that of rolling
(d) all the above

Dheeraj Sharma

Numerade Educator

Problem 37

A sphere of radius $R$ is rolling on a rough horizontal surface. The magnitude of velocity of $A$ with respect to ground will be :(a) $\sqrt{2} v_{\mathrm{cm}}$
(b) $2 v_{\mathrm{cm}} \sin \theta$
(c) $\sqrt{2} v_{\mathrm{cm}} \sqrt{1+\sin \theta}$
(d) no sufficient information

Dheeraj Sharma

Numerade Educator

Problem 38

When a wheel moves a distance shorter than $2 \pi R$ while making one rotation, then:
(a) $v_{\mathrm{cm}}<R \omega$
(b) $v_{\mathrm{cm}}<R \omega$
(c) $v_{\mathrm{cm}}>R \omega$
(d) $v_{\mathrm{cm}}>R \omega$

Dheeraj Sharma

Numerade Educator

Problem 39

If a body moves through a distance greater than $2 \pi R$ in one full rotation. Then:
(a) $v_{\mathrm{cm}}>R \omega$
(b) $v_{\mathrm{cm}}<R \omega$
(c) $v_{\mathrm{cm}}>R \omega$
(d) $v_{\mathrm{cm}}<R \omega$

Dheeraj Sharma

Numerade Educator

Problem 40

A circular disc of radius $R$ rolls without slipping along the horizontal surface with constant velocity $v_{0}$. We consider a point $A$ on the surface of the disc. Then the acceleration of the point $A$ is:
(a) constant
(b) constant in magnitude
(c) constant in direction
(d) constant in magnitude as well as direction

Saman Zulfiqar

Numerade Educator

Problem 41

The bobbin with thread around it lies on a horizont floor and can roll along it without slipping. Both pulle $P_{1}$ and $P_{2}$ are light and frictionless. The pulley $P_{1}$ mov downwards with constant velocity $v_{0}$. The velocity centre of mass of bobbin is :
(a) $\frac{v_{0} R}{R-r}$ in forward direction
(b) $\frac{2 v_{0} R}{R-r}$ in backward direction
(c) $\frac{v_{0} R}{R-r}$ in backward direction
(d) $\frac{2 v_{0} R}{R-r}$ in forward direction

Dheeraj Sharma

Numerade Educator

Problem 42

In the given figure, the sphere rolls without slipping on the plank which is moving with constant velocity $v_{0}$ - The radius and angular velocity of the sphere is $r$ and $\omega$ respectively. The velocity of centre of mass of the sphere is:
(a) $v_{0}+r \omega$
(b) $v_{0}-r \omega$
(c) $r \omega$
(d) $v_{0}$

Dheeraj Sharma

Numerade Educator

Problem 43

In the given figure, a solid sphere is placed on a plank having acceleration $a_{0}$ (shown in the figure). Then:
(a). if $a_{p}=a_{0}$, pure rolling takes place
(b) if $v_{p}=v_{0}$ pure rolling takes place
(c) if $a_{p}=a_{0}, v_{p} \neq v_{0}$ pure rolling takes place
(d) if $a_{p}=a_{0}, v_{p}=v_{0}$, pure rolling takes place

Dheeraj Sharma

Numerade Educator

Problem 44

In the given figure, for pure rolling of spheres:
(a) friction on $B$ is in forward direction
(b) friction on $A$ is in backward direction
(c) friction on $A$ and $B$ are in forward direction
(d) both (a) and (c) are correct

Dheeraj Sharma

Numerade Educator

Problem 45

A uniform sphere of radius $a$ rotating with an angular velocity $\omega$ about an axis perpendicular to the plane of motion and its centre impinges on a horizontal plane, let $u$ and $v$ are horizontal and vertical component of velocity before impact. Then:
(a) if $u=a \omega, u$ and $\omega$ are unaltered
(b) if $u=a \omega$, surface is frictionless
(c) if $u>a \omega$, angular velocity increases
(d) all the above

Saman Zulfiqar

Numerade Educator

Problem 46

An imperfectly rough sphere moves from rest down a plane inclined at an angle $\alpha$ to the horizontal. The coefficient of friction between the inclined plane and sphere is $\mu$. Then
(a) if $\mu<\frac{2}{7} \tan \alpha$, then the sphere never rolls
(b) if $\mu=\frac{2}{7} \tan \alpha$, then the maximum friction always being exerted
(c) $\mu>\frac{2}{7} \tan \alpha$, then pure rolling takes place
(d) all the above

Dheeraj Sharma

Numerade Educator

Problem 47

A ball rolls down an inclined groove acquiring a velocity $v_{f}$ as it reaches the bottom. If the same ball slides without friction rather than rolled from the same height down a similai $^{4} \ldots_{-2}$ following statements is true?
(a) $v_{f}<v_{s}$ because work must be done by the rolling ball against frictional forces
(b) $v_{f}>v_{6}$ because the rotational kinetic energy acquired makes the rolling ball travel faster
(c) $v_{f}=v_{s}$ because K.E. must be conserved
(d) $v_{f}<v_{s}$ because the rolling ball acquires rotational as well as translational K.E.

Saman Zulfiqar

Numerade Educator

Problem 48

A rod $A B$ of mass $10 \mathrm{~kg}$ tied with a string at $C$ such that $A C=A B$. A $\theta=30^{\circ}:$
(a) rod is in equilibrium
(b) the force of friction on the rod by ground is $25 \mathrm{~N}$
(c) the force of friction acts in the forward direction
(d) all the above

Dheeraj Sharma

Numerade Educator

Problem 49

In the given figure:
(a) if ball performs pure rolling then friction in surface is absent
(b) if air resistance is absent, after point $A$, angular momentum of ball remains constant
(c) after $A$, path of centre of mass is parabolic
(d) both (b) and (c) are correct

Dheeraj Sharma

Numerade Educator

Problem 50

A uniform rod is placed vertically on a smooth surface and then released. Then:
(a) the centre of mass of rod follows straight line path
(b) the centre of mass of rod follows circular path
(c) the instantaneous axis is passing through the contact point
(d) all the above

Dheeraj Sharma

Numerade Educator

Problem 51

Three links are hinged together to form a triangle $A B C$ as shown in the figure. At a certain instant, the point $A$ is moving towards the mid point of $B C$ with a velocity of $5 \mathrm{~m} / \mathrm{s}$ and $B$ is moving at a perpendicular direction to $A C$. The velocity of point $C$ is :
(a) $5 \mathrm{~m} / \mathrm{s}$
(b) $10.4 \mathrm{~m} / \mathrm{s}$
(c) $10.8 \mathrm{~m} / \mathrm{s}$
(d) $1.8 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma

Numerade Educator

Problem 52

A ball rolls off the top of a step ladder with a horizontal velocity of $10 \mathrm{~m} / \mathrm{s}$. If the steps are $1 \mathrm{~m}$ high and $1 \mathrm{~m}$ wide, the ball will just hit:
(a) 3rd step
(b) 20 th step
(c) 12 th step
(d) 10th step

Saman Zulfiqar

Numerade Educator

Problem 53

A cylinder of mass $m$ rests in a carriage shown. The maximum acceleration of carriage so that the cylinder does not loose contact at $B$ is :
(a) $3.66 \mathrm{~m} / \mathrm{s}^{2}$
(b) $10 \mathrm{~m} / \mathrm{s}^{2}$
(c) $45 \mathrm{~m} / \mathrm{s}^{2}$
(d) $8 \mathrm{~m} / \mathrm{s}^{2}$

Dheeraj Sharma

Numerade Educator

Problem 54

Mark correct option or options:
(a) Rolling friction always oppose the motion of centre of mass of rolling body
(b) Sliding friction always oppose the motion of centre of mass of rolling body
(c) Rolling friction depends upon hardness of the surface
(d) Rolling friction does not depend upon roughness of the surface
(e) (a), (c) and (d) are correct

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 55

Mark correct option or options:
(a) A uniform cube has minimum moment of inertia about an axis passing through centre and is passing through opposite corners
(b) The moment of inertia of a complicated shape bodies can be determined by using inertia of table
(c) Displacing of axial vectors is meaningless
(d) All the above

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 56

A uniform cube of mass $m$ and edge $a$ moves on a horizontal surface along the positive $x$ -axis, with initial velocity $v_{0}$ :
(a) during motion, $N>m g$
(b) during motion, normal reaction acts on the centre of mass
(c) during motion, the normal reaction shifts towards positive $x$ -axis from the centre of mass
(d) during motion, normal reaction shifts in the direction of the forces of friction

Saman Zulfiqar

Numerade Educator

Problem 57

In the case of toppling of the body about the point $A$. (Shown in the figure):
(a) $v_{C}>v_{2}>v_{1}>v_{A}$
(b) $v_{1}>v_{2}>v_{C}>v_{A}$
(c) $v_{A}>0$
(d) $v_{C}<v_{1}<v_{2}<v_{A}$

Dheeraj Sharma

Numerade Educator

Problem 58

In the above problem, acceleration of the point $A$ is :
$(a)>0$
(b) $\geq 0$
(c) $<0$
$(\mathrm{d})=0$

Dheeraj Sharma

Numerade Educator

Problem 59

Two cubes $A$ and $B$ of same shape, size and mass are placed on a rough surface in the same manner. Equal forces are applied on both the cubes. But at the cube $A$, the force is applied at the top in horizontal direction. But at the cube $B$ just above the centre of mass of the cube in the same manner. Then:
(a) $A$ will topple first
(b) $B$ will topple first
(c) both wili topple at the same time
(d) none of the above

Dheeraj Sharma

Numerade Educator

Problem 60

A cube of side $a$ is placed on rough surface (shown in the figure). Then:
(a) if $f<\frac{M g}{2}$, then the body will move in pure rotation and will not topple
(b) if $F>\frac{M g}{2}$, the body will topple
(c) if $\mu>0.5$, the body will move by toppling
(d) all the above

Dheeraj Sharma

Numerade Educator

Problem 61

For the toppling of the shown regular hexagon, the coefficient of friction must be:
(a) $>0.21$
(b) $<0.21$
(c) $=0.21$
(d) $<0.21$

Dheeraj Sharma

Numerade Educator

Problem 62

A regular polygon of $n$ sides is placed on a rough surfac vertically as such one of the side of regular polygor touches the surface. A force is applied horizontally at th top. The chosen value of $n$ are 3,5 and 8 . For which valu of $n$, the polygon first is likely to topple?
(a) 3
(b) 5
(c) 8
(d) all the above

Dheeraj Sharma

Numerade Educator

Problem 63

A particle performs uniform circular motion with an angular momentum $L$. If the frequency of particle motion is doubled and its K.E. is halved, the angular momentum becomes:
(a) $2 L$
(b) $4 L$
(c) $\frac{L}{2}$
(d) $\frac{L}{4}$

Dheeraj Sharma

Numerade Educator

Problem 64

$L=$ I\omega formula is :
(a) always correct
(b) sometimes correct
(c) always wrong
(d) physically correct but dimensionally wrong

Dheeraj Sharma

Numerade Educator

Problem 65

A person can balance easily a moving bicycle, but cannot balance a stationary bicycle. This statement is based upon:
(a) conservation principle of linear momentum
(b) conservation principle of angular momentum
(c) conservation principle of energy
(d) all of the above principle

Saman Zulfiqar

Numerade Educator

Problem 66

Mark correct option or options
(a) The angular momentum of a rotating body must be parallel to the angular velocity
(b) The angular momentum may or may not be parallel to angular velocity
(c) The kinetic energy of rotational body is half of product of angular momentum and angular velocity
(d) Both (b) and (c) are correct

Vysakh M

Numerade Educator

Problem 67

A particle is projected with initial velocity $u$ at an angle $\alpha$ above the horizontal, then variation of torque and angular momentum with time will be :

Dheeraj Sharma

Numerade Educator

Problem 68

If a particle of mass $m$ is projected at an angle $\alpha$ with the horizontal, then :
(a) the angular momentum remains constant
(b) the linear momentum of particle remains constant
(c) total mechanical energy remains constant in the absence of air resistance
(d) all the above

Saman Zulfiqar

Numerade Educator

Problem 69

A mass $m$ is moving with a constant velocity along a line parallel to the $x$ -axis, away from the origin. Its angular momentum with respect to the origin:
(a) is zero
(b) remains constant
(c) goes on increasing
(d) goes on decreasing

Saman Zulfiqar

Numerade Educator

Problem 70

When a body is projected at an angle with the horizontal in the uniform gravitational field of the earth, the angular momentum of the body about the point of projection, as it proceeds along its path:
(a) remains constant
(b) increases
(c) decreases
(d) initially decreases and increases after its highest point

Saman Zulfiqar

Numerade Educator

Problem 71

A particle of mass $m$ is projected with velocity $v$ moving at an angle of $45^{\circ}$ with horizontal. The magnitude of angular momentum of projectile about point of projection when particle is at maximum height, is :
(a) zero
(b) $\frac{m v^{3}}{4 \sqrt{2} g}$
(c) $\frac{m v^{3}}{\sqrt{2} g}$
(d) $m \sqrt{2} g h^{3}$

Saman Zulfiqar

Numerade Educator

Problem 72

A man is standing at the centre of a big flat disc which is rotating with angular speed $\omega .$ The man starts running with ac* apration $a$ with respect to disc. If $M, m, I, R$ are mass of disc, mass of man, M.I. of disc and radius of disc respectively, the angular acceleration of disc when man is at a distance $x$ from centre is :
(a) $\frac{I \omega}{\left(1+m x^{2}\right)} 2 m x \sqrt{2} a x$
(b) $\frac{I \omega}{\left(1+m x^{2}\right)^{2}} \sqrt{2} a x$
(c) $\frac{I \omega}{\left(1+m x^{2}\right)^{2}} 2 m x \sqrt{2} a x$
(d) none of these

Dheeraj Sharma

Numerade Educator

Problem 73

A lady dancer is dancing on a turn table. During dancing, she stretches her hands. Then :
(a) the angular velocity increases
(b) the angular velocity decreases
(c) the angular velocity first increases, then decreases
(d) the angular velocity remains constant

Saman Zulfiqar

Numerade Educator

Problem 74

Two particles, each of mass $m$ and moving with speed $v$ in opposite directions along parallel lines are separated by a distance $d$. The vector angular momentum of this system of the particles will be :
(a) maximum when the origin is taken beyond the two parallel lines on either sides
(b) maximum when the origin is taken beyond the two parallel lines on either sides
(c) maximum when the origin is taken beyond the two parallel lines on either sides
(d) same, no point is taken as the origin

Saman Zulfiqar

Numerade Educator

Problem 75

A uniform rod of length $2 a$ is held with one end resulting on a smooth horizontal table making an angle $\alpha$ with the vertical. When the rod is released:
(a) its centre of mass moves vertically downwards on a straight line
(b) its centre of mass remains in rest
(c) the-rod rotates about a vertical axis
(d) both (a) and (c) are correct

Saman Zulfiqar

Numerade Educator

Problem 76

A $70 \mathrm{~kg}$ man standing on ice throws a $3 \mathrm{~kg}$ body horizontally at $8 \mathrm{~m} / \mathrm{s}$. The friction coefficient between the ice and his feet is $0.02$. The distance, the man slips is:
(a) $0.3 \mathrm{~m}$
(b) $2 \mathrm{~m}$
(c) $1 \mathrm{~m}$
(d) $\infty$

Saman Zulfiqar

Numerade Educator

Problem 77

In a radioactive decay, a number of fragments are found. If parent nucleus is initially at rest then after decay centre of mass will :
(a) move on a straight line
(b) move in a circle
(c) remain in rest
(d) move in parabolic path

Vysakh M

Numerade Educator

Problem 78

A particle of mass $m$ strikes elastically, a rod of mass $M$ and length $L$ suspended from a fixed support, then:
(a) conservation of linear momentum can be applied
(b) conservation of angular momentum can be applied
(c) both the above
(d) none of the above

Saman Zulfiqar

Numerade Educator

Problem 79

A weightless rod of length $l$ carries two equal masses $m$ one fixed at the end and other in the middle of the rod. The rod can revolve in a vertical plane about $A$. Then horizontal velocity which must be imparted to end $C$ of rod to deflectit to horizontal position is:
(a) $\sqrt{\frac{12}{5} g l}$
(b) $\sqrt{3 g} l$
(c) $\sqrt{\frac{16}{5} g l}$
(d) $\sqrt{2 g} \bar{l}$

Saman Zulfiqar

Numerade Educator

Problem 80

Two balls $A$ and $B$ of angular velocities $\omega_{A}$ and $\omega_{B}$ collide with each other. Then after collision:
(a) both have same angular velocities
(b) $\omega_{A}>\omega_{B}$
(c) $\omega_{A}=\omega_{B}$, when balls are smooth
(d) $\omega_{A}>\omega$ - when balls are smooth

Saman Zulfiqar

Numerade Educator

Problem 81

A uniform solid cylinder rolling without slipping along a horizontal plane suddenly encounters a plane inclined at angle $\theta$ as shown in figure. The value of $\theta$ which could bring the cylinder immediately to rest after impact, is :
(a) $90^{\circ}$
(b) $60^{\circ}$
(c) $120^{\circ}$
(d) $30^{\circ}$

Vysakh M

Numerade Educator

Problem 82

A body whose mass is $m_{1}$ is acted upon at a given point $P$ by a blow of impulse $x$. If $v$ and $v^{\prime}$ be the velocities of $P$ in the direction of $x$ just before and just after the action of $x$, the change in kinetic energy is:
(a) $\left(\frac{v+v^{\prime}}{2 x}\right)$
(b) $\frac{\left(v+v^{\prime}\right) x}{2}$
(c) $\frac{1}{4}\left(v^{\prime}+v\right) x$
(d) all of these

Vysakh M

Numerade Educator

Problem 83

A uniform rod $O A$ of mass $M$ and length $2 \pi$ rests on a smooth table and is free to turn about a smooth pivot at its end $O$, in contact with it at a distance $b$ from $O$ is an inelastic particle of mass $m$, a horizontal blow of impulse $p$ is given to rod at a distance $x$ from $O$ in a direction perpendicular to the rod. The resultant instantaneous angular velocity of the rod is:
(a) $\frac{p x}{\frac{4 M a^{2}}{3}+m b^{2}}$
(b) $\frac{p x}{M}$
(c) $\frac{p x}{m a^{2}+m b^{2}}$
(d) none of these

Saman Zulfiqar

Numerade Educator

Problem 84

A uniform rod $A B$ of mass $m$ and length $l$ is at rest on a smooth horizontal surface. An impulse $p$ is applied to the end $B$. The time taken by the rod to turn through a right angle is :
(a) $2 \pi \frac{m l}{p}$
(b) $2 \pi \frac{p}{m l}$
(i) $\frac{\pi m l}{12 p}$
(d) $\frac{\pi p}{m !}$

Saman Zulfiqar

Numerade Educator