A solid sphere, a hollow sphere, and a disc, all having the same mass and radius, are placed at the top of a smooth incline and released. Least time will be taken in reaching the bottom by 

1.  the solid sphere

2.  the hollow sphere

3.  the disc

4.  all will take the same time  

 

Two bodies with moment of inertia $I_2 and I_2$(such that $I_1>I_2$) have equal angular velocity.  If their kinetic energy of rotation are $E_1 and E_2$ then [Pb. PET 2000]

1. $E_1\ge E_2$                             

2. $E_1>E_2$

3. $E_1<E_2$                             

4. $E_1=E_2$ 

A man is sitting on a rotating table with his arms stretched outwards.  When he suddenly folds his arms inside, then

1. his angular velocity will decrease

2. his angular velocity remains constant

3. his moment of inertia decreases

4. angular momentum increases

A wheel of radius R rolls on the ground with a uniform velocity v. The velocity of topmost point relative to the bottommost point is

1. v

2. 2v

3. v/2

4. zero

If the net external forces acting on the system of particles is zero, then which of the following may vary ?

1. Momentum of the system

2. Velocity of centre of mass

3. Position of centre of mass

4. None of the above

A wheel is rotating about an axis through its centre at \(720\) r.p.m. It is acted upon by a constant torque opposing its motion for \(8\) seconds to bring it to rest finally. The value of torque in N-m is: (given \(I\) = $\frac{24}{\mathrm{\pi }}$ kg ${\mathrm{m}}^2$)
1. \(48\)
2. \(72\)
3. \(96\)
4. \(120\)

A wheel is rotating 900 rpm about its axis. When power is cut off it comes to rest in 1 min. The angular retardation in rad/s² is 

1. $\mathrm{\pi }/2$

2. $\mathrm{\pi }/4$

3. $\mathrm{\pi }/6$

4. $\mathrm{\pi }/8$

An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver ?

1. 350 N-m

2. 440 N-m

3. 531 N-m

4. 628 N-m

In an orbital motion, the angular momentum vector is 

1. Along the radius vector

2. Parallel to the linear momentum

3. In the orbital plane

4. Perpendicular to the orbital plane

A wheel is at rest. Its angular velocity increases uniformly and becomes 80 rad/s after 5 s. The total angular displacement is 

1. 800 rad

2. 400 rad

3. 200 rad

4. 100 rad