In the rotational motion, different particles of the body have :

• both linear and angular velocities equal

• linear velocities equal but different angular velocities

• angular velocities equal but different linear velocities

• both linear and angular velocity different

The moment of inertia of a ring about one of its diameter is I. What will be its moment of inertia about a tangent parallel to the diameter?

• $\frac{4}{3}$ I

• 2 I

• $\frac{3}{2}$ I

• 3 I

A disc, initially at rest, starts rotating about its own axis, with a constant angular acceleration of 0.2 rad/s². The time taken by the disc to rotate by 10 rad is (in second)

• 7.07

• 10

• 14.14

• 100

A disc of a siren containing 60 holes rotates at a constant speed of 360 rpm. The emitted sound is in unison with a tuning fork of frequency

• 10 Hz

• 360 Hz

• 216 Hz

• 60 Hz

A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then the relation between the moments of inertia I_X and I_Y is

• I_Y = 321_X

• I_Y = 161_X

• I_Y = I_X

• I_Y = 641_X

The moments of inertia of two freely rotating bodies A and B are I_A and I_B respectively I_A > I_B and their angular momenta are equal. If K_A and K_B are their kinetic energies then

• K_A = K_B

• K_A > K_B

• K_A < K_B

• K_A = 2 K_B

If the earth is treated as a sphere of radius R and mass M, its angular momentum about the axis of rotation with time period T is

• $\frac{{\mathrm{\pi MR}}^2}{\mathrm{T}}$

• $\frac{{\mathrm{MR}}^2\mathrm{T}}{2\mathrm{\pi }}$

• $\frac{2{\mathrm{\pi MR}}^2}{\mathrm{T}}$

• $\frac{4{\mathrm{\pi MR}}^2}{5\mathrm{T}}$

Angular velocity of second hand of a clock is

• $\frac{\mathrm{\pi }}{30} \mathrm{rad}/\mathrm{s}$

• $\frac{\mathrm{\pi }}{60} \mathrm{rad}/\mathrm{s}$

• $\frac{\mathrm{\pi }}{15} \mathrm{rad}/\mathrm{s}$

• $\frac{\mathrm{\pi }}{2} \mathrm{rad}/\mathrm{s}$

Sphere, disc and ring are allowed to roll down on an inclined plane from its top, then order in which they reach at the bottom will be

• ring, disc, sphere

• sphere, disc, ring

• disc, ring, sphere

• sphere, ring, disc

If we made half the radius of earth, then duration of day will become

• 6 h

• 12 h

• 24 h

• 3 h