Two bodies of moments of inertia I₁ and I₂ (I₁ > I₂) have equal angular momentum. If E₁ and E₂ are their kinetic energies of rotation, then

• E₁ > E₂

• E₁ = E₂

• E₁ < E₂

• Cannot be said

A coin placed on a rotating turntable just slips if it is placed at a distance of 8 cm from the centre. If angular velocity of the turntable is doubled, it will just slip at a distance of :

• 1 cm

• 2 cm

• 4 cm

• 8 cm

A solid sphere is rotating about a diameter at an angular velocity ω. If it cools so that its radius reduces to $\frac{1}{\mathrm{n}}$ of its original value, its angular velocity becomes:

• $\frac{\mathrm{\omega }}{\mathrm{n}}$

• $\frac{\mathrm{\omega }}{{\mathrm{n}}^2}$

• nω

• ${\mathrm{n}}^2\mathrm{\omega }$

Five particles of mass 2 kg are attached to the rim of a circular disc of radius 0.1 m and negligible mass. Moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane is

• 1 kg m²

• 0.1 kg m²

• 2 kg m²

• 0.2 kg m²

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