Rotational Work and Energy

Q. A metal stick of mass $1$ kg and length 1 metre is held vertically with one end on the floor and is then allowed to fall. All values are in SI units. Take approximations.
$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(a) Initial mechanical energy}& \text{(p)}5.425\\ {\text{(b)(Angular velocity)}}^2\text{just before hitting the ground}& \text{(q) 29.429}\\ \text{(c) Linear velocity of the free end just before hitting the ground}& \text{(r) 4.9}\\ \text{(d) Moment of inertia}& \text{(s) 0.333}\end{array}$

1. $a-p;b-q;c-r;d-p$
2. $a-r;b-q;c-p;d-s$
3. $a-q;b-r;c-p;d-s$
4. $a-r;b-q;c-s;d-p$

Q. A flywheel of moment of inertia $0.32kg-m^2$ is rotated steadily at 120 rad/sec by an electric motor. The kinetic energy of the flywheel is

1. 4608 J
2. 2304 J
3. 6912 J
4. 1152 J

Q. Two bodies rotating with the same angular momentum have M.I. $I_{1}and{I}_2$ respectively such as $I_1>I_2$ respectively, then

1. $E_2>E_1$
2. $E_2=E_1$
3. $E_1>E_2$
4. $E_1=2E_2$

Q. If the angular momentum of a rotating body is increased by $200\%,$ then its kinetic energy of rotation will be increased by

1. 
2. 
3. 
4. 

Q. A solid sphere of mass M and radius R is rolling on a horizontal surface without sliding with a velocity v. The ratio of its rotational and linear kinetic energies is

1. 2 : 5
2. 5 : 2
3. 7 : 10
4. 2 : 7

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. 
2. 
3. 
4. 

Q. A ring of radius 0.5 m and mass 10 kg is rotating about its diameter with an angular velocity of 20 rad/s. Its kinetic energy is

1. 250 J
2. 500 J
3. 10 J
4. 100 J

Q. If each point mass of a rigid ring covers a distance of $\frac{\pi }{2}m,$ by how much angle (in radians) the ring has been rotated? (R = 2m)

1. $\frac{\pi }{2}radians$
2. $\frac{\pi }{4}radians$
3. $\pi$ radians
4. $\frac{3\pi }{4}radians$

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.

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. 

2. 

3. 

4.