Rotational Work and Energy

Q. The unit of length, velocity and force are doubled. which of the following is the correct change in the other units? A) unit of time is doubled B) unit of mass is doubled C) Unit of momentum is doubled D) unit of energy is doubled

Q. A body of moment of inertia of $3kg-m^2$ is rotating with an angular velocity of 2 rad/sec and has the same kinetic energy as a mass of 12 kg moving with a velocity of

1. 8 m/s
2. 0.5 m/s
3. 2 m/s
4. 1 m/s

Q. Two bodies of different masses m1 and m2 have equal momentum. Their k.E are in what ratio and why

Q. A rigid body is made up of three identical thin rods $A,B$ and $C$, each of length $L$ fastened together in the form of letter $H$. The body is free to rotate about a horizontal axis that runs along the length of one of the legs ($A$) of the body $H$. The body is allowed to fall from rest from a position in which the plane of $H$ is horizontal. What is the angular speed of the body when the plane of $H$ becomes vertical?

1. $\sqrt{\frac{g}{L}}$
2. $\frac{1}{2}\sqrt{\frac{g}{L}}$
3. $\frac{3}{2}\sqrt{\frac{g}{L}}$
4. $2\sqrt{\frac{g}{L}}$

Q. 23.A body is projected at angle 30 degree with the horizontal with momentum p. At its highest point the magnitude of momentum is

Q. A block of mass $m$ is suspended from a pulley in the form of a circular disc of mass $m$ and radius $R$. The system is released from rest. Find the angular velocity of the disc when the block has dropped by height $h$. [Assume there is no slipping between string & pulley]

1. $\frac{1}{R}\sqrt{\frac{4gh}{3}}$
2. $\frac{1}{R}\sqrt{\frac{2gh}{3}}$
3. $R\sqrt{\frac{2gh}{3}}$
4. $R\sqrt{\frac{4gh}{3}}$

Q. Two identical hollow spheres having mass $m=3\text{kg}$ and radius $r=1\text{m}$ are performing combined translational and rotational motion as shown in the figure. If $\omega =2\text{rad/s}$, $v_{com}=3\text{m/s}$ and ${\omega }^{\prime }=3\text{rad/s},v_{com}^{{}^{\prime }}=2\text{m/s}$, find the ratio of their kinetic energies.

1. $\frac{3}{7}$
2. $\frac{7}{6}$
3. $\frac{8}{7}$
4. $\frac{3}{5}$

Q.

A small ball is projected along the surface of a smooth inclined plane with speed 10 m/s along the direction shown at t = 0. the point of projection is origin, z - axis is along vertical . The accelearation due to gravity is 10 m/ $s^2$. Lists values of certain parameters related to motion of ball and column - II linst fifferent time instants. Match appropriately.

"$$\begin{array}{cc}coloumn1& coloumn2\\ \left(p\right)Distancefromx-axis& \left(a\right)0.5\\ \left(q\right)Speedisminimum& \left(b\right)1.0\\ \left(r\right)Velocitymakesangel{37}^{\circ }withx-axis& \left(c\right)1.50\\ \left(s\right)Ballismaximumawayfromx-axis& \left(d\right)2.0\end{array}$$

1. p - a, c; q - b; r - d; s - b

2. p - b; q - a, d; r - d; s - b

3. p - d; q - b; r - a, b; s - a

4. p - a; q - c; r - d; s - b

Q. Two equal masses m are projected at the same angle from two points separated by their range withequal velocities.The momentum at the point of collision is ??

Q. 37. A particle of mass 5g is moving in a circle of radius 0.5m with an angular velocity of 6rad/s find the change in linear velocity in half a revolution , the magnitude of the acceleration of the particle

Q.

In the shown figure, a particle of mass 'm' slides down the frictionless surface from height 'h' and collides with the uniform vertical rod of length L and mass M. After the collision, mass m sticks to the rod. The rod is free to rotate in a vertical plane about a fixed axis through O. Find the cosine of the maximum angular deflection of the rod from its initial position.

1. $1-\frac{m^2{v}_0^2}{2(m+\frac{M}{3})(m+\frac{M}{2})gL}$

2. $1-\frac{M^2{v}_0^2}{2(m+\frac{M}{3})(m+\frac{M}{2})gL}$

3. $1-\frac{m^2{v}_0^2}{(m+\frac{M}{3})(m+\frac{M}{2})gL}$

4. $1-\frac{M^2{v}_0^2}{(m+\frac{M}{3})(m+\frac{M}{2})gL}$

Q. The radius of a rotating sphere decreases by $2\%$ keeping the mass constant, the change in its rotational kinetic energy?

1. $2\%$
2. $1\%$
3. $8\%$
4. $4\%$

Q. the magnitude of change in velocity of a particle having speed v is v during a time interval △ t while moving in a uniform circular motion. the magnitude of avg force on the body is proportional to?

Q. KE of a body is increased by 44%. What is thepercent increase in the momentum?(1) 10%(2) 20%ac(3) 30%(4) 44%

Q. the angular momentum of aparticle performing uniform circular motion is L .If the K.E. of particle is doubled and frequency ia halved then angular momentum becomes

Q.

the magnitude of change in velocity of a particle having speed v is, v during a time interval △ t while moving in a uniform circular motion.The magnitude of average force on the particle is proportional to:

Q. A solid cylinder is rolling without sliding. What fraction of its total kinetic energy is associated to rotational motion ?

1. $\frac{1}{2}$
2. $\frac{1}{3}$
3. $\frac{1}{4}$
4. $\frac{1}{5}$

Q. The unit of length, velocity and force are doubled.Which of the following is the correct change in the other units?1.unit of time is doubled2.unit of mass is doubled3.unit of momentum is doubled4.unit of energy is doubled

Q. a rod of (lets lay mass M) is attached to a hinge at one end. If a particle of mass m hand velocity u hits the other end. Then what happens to Conservation of Linear Momentum. Why isnt it applicable in this case?

Q. a disc of moment of inertia $\frac{9.8}{{\pi }^2}kg-m^2$ is rotating at 600 rmp. If the frequency of rotation changes from 600 rpm to 300 rpm, then what is the work done?

1. 1467 J
2. 1452 J
3. 1567 J
4. 1632 J

Q. A small object of uniform density rolls up a curved surface with an initial velocity $v$. It reaches upto a maximum height of $\frac{3v^2}{4g}$ with respect to initial position. The object is a

1. Ring
2. Solid sphere
3. Hollow sphere
4. Disc

Q. A body is rotating with angular momentum L. If I is its moment of inertia about the axis of rotation, its kinetic energy of rotation is?

1. $\frac{1}{2}I{L}^2$
2. $\frac{1}{2}IL$
3. $\frac{1}{2}\left(I^2/L\right)$
4. $\frac{1}{2}\cdot \frac{L^2}{I}$

Q. Below is the graph for $\tau =2\sin \theta$. calculate work done by the torque till $\theta =\pi .$

1. $2\text{J}$
2. $4\text{J}$
3. $0\text{J}$
4. $2\pi \text{J}$

Q. A uniform circular disc of radius 'R' with a concentric circular hole of radius $\frac{R}{2}$ rolls on a horizontal plane. The fraction of its total energy associated with its rotational motion is

1. $\frac{1}{4}$
2. $\frac{5}{13}$
3. $\frac{1}{2}$
4. $1$

Q. A solid sphere of radius ${}^{\prime }{r}^{\prime }$ and mass ${}^{\prime }{m}^{\prime }$ is rotating about an axis passing through its COM with an angular speed ${}^{\prime }{\omega }^{\prime }$ and has rotational kinetic energy $k_1$. If the radius of the sphere is halved and angular speed is doubled, then its rotational kinetic energy becomes $k_2$. Which of the following options is correct ?

1. $k_1>k_2$
2. $k_1<k_2$
3. $k_1=k_2$
4. $k_1=k_2=0\text{J}$

Q. Two blocks A and B of masses 10 kg and 5 kgrespectively are placed inside a cart which is movinghorizontally with an acceleration of 2 m/s as shownin the figure. If all the surfaces are smooth then the3.ratio of normal reaction between the block A andvertical surface of the cart and normal reactionbetween the blocks A and B is2a = 2 m/sABAFP(1) 3:1(2) 2:3(3) 2: 1(4) 1:2

Q. A solid sphere mass $M$ and radius $R$ rolls on a horizontal surface without slipping. The ratio of rotational $K.E.$ ro total $K.E.$ is:-

1. $\frac{1}{2}$
2. $\frac{3}{7}$
3. $\frac{2}{7}$
4. $\frac{2}{10}$

Q. Obtain an expression for total kinetic energy of a rolling body in the form $\frac{1}{2}M{V}^2[1+\frac{K^2}{R^2}]$.

Q. A body of moment of inertia of $3kg-m^2$ is rotating with an angular velocity of 2 rad/sec and has the same kinetic energy as a mass of 12 kg moving with a velocity of

1. 8 m/s
2. 0.5 m/s
3. 2 m/s
4. 1 m/s

Q. Two plates 1 and 2 move with velocities $v$ and $2v$ as shown. If the sphere does not slide relative to the plates and assuming the mass of each body as $m$, find the kinetic energy of the system (plates + sphere).

1. $\frac{123}{40}m{v}^2$
2. $\frac{230}{40}m{v}^2$
3. $\frac{123}{40}m{v}^3$
4. $\frac{120}{50}m{v}^2$