A sphere of diameter 0.2 m and mass 2 kg is rolling on an inclined plane with velocity v = 0.5 m/s. The kinetic energy of the sphere is :

• 0.1 J

• 0.3 J

• 0.5 J

• 0.42 J

A sphere rolls down an inclined plane of inclination θ. What is the acceleration as the sphere reaches the bottom?

• $\frac{5}{7}\mathrm{g} \mathrm{sin\theta }$

• $\frac{3}{5}\mathrm{g} \mathrm{sin\theta }$

• $\frac{2}{7}\mathrm{g} \mathrm{sin\theta }$

• $\frac{2}{5}\mathrm{g} \mathrm{sin\theta }$

In a bicycle, the radius of rear wheel is twice the radius of front wheel. If r_f and r_r are the radii, v_f and v_r are the speeds of topmost points of the wheel, then:

• v_r = 2v_f

• v_f = 2v_r

• v_r = v_f

• v_f > v_r

Moment of inertia of an object does not depend upon :

• mass of the object

• mass distribution

• angular velocity

• axis of rotation

Two spherical shells one which is placed in air has constant charge Q; and the other which is placed in a medium of dielectric constant K has a charge Q;­ The ratio of forces between the shell is:

• K : 1

• 1 : K

• K² : 1

• 1 : K²

The mass of a solid sphere is 2 kg and radius is 10 cm. Sphere, tied to one end of 1 m long string, is rotated at a rate of 10 rad/sec. The rotational kinetic energy of sphere is :

• 121.4 J

• 18.5 J

• 15.2 J

• 22.0 J

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

140.

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