91Ó°ÊÓ

A thin uniform circular ring is rolling down an inclined plane of inclination \(30^{\circ}\) without slipping. Its linear acceleration along the inclined plane will be (a) \(g / 2\) (b) \(\mathrm{g} / 3\) (c) \(g / 4\) (d) \(2 \mathrm{~g} / 3\)

A solid sphere of mass \(0.1 \mathrm{~kg}\) and radius \(2 \mathrm{~cm}\) rolls down an inclined plane \(1.4 \mathrm{~m}\) in length (slope in 10). Starting from rest its final velocity will be (a) \(1.4 \mathrm{~m} / \mathrm{sec}\) (b) \(0.14 \mathrm{~m} / \mathrm{sec}\) (c) \(14 \mathrm{~m} / \mathrm{sec}\) (d) \(0.7 \mathrm{~m} / \mathrm{sec}\)

A solid sphere rolls down an inclined plane and its velocity at the bottom is \(v_{1}\). Then same sphere slides down the plane (without friction) and let its velocity at the bottom be \(v_{2}\). Which of the following relation is correct (a) \(v_{1}=v_{2}\) (b) \(v_{1}=\frac{5}{7} v_{2}\) (c) \(v_{1}=\frac{7}{5} v_{2}\) (d) None of these

A cord is wound round the circumference of wheel of radius \(r\). The axis of the wheel is horizontal and moment of inertia about it is \(I\). A weight \(m g\) is attached to the end of the cord and falls from rest. After falling through a distance \(h\), the angular velocity of the wheel will be (a) \(\sqrt{\frac{2 g h}{I+m r}}\) (b) \(\sqrt{\frac{2 m g h}{I+m r^{2}}}\) (c) \(\sqrt{\frac{2 m g h}{I+2 m r^{2}}}\) (d) \(\sqrt{2 g h}\)

{ A block of mass } 2} 2 \mathrm{~kg}\( hangs from the rim of a wheel of radius \)0.5 \mathrm{~m} .\( On releasing from rest the block falls through \)5 \mathrm{~m}\( height in \)2 s .\( The moment of inertia of the wheel will be (a) \)1 \mathrm{~kg}-\mathrm{m}^{2}\( (b) \)3.2 \mathrm{~kg}-\mathrm{m}^{2}\( (c) \)2.5 \mathrm{~kg}-\mathrm{m}^{2}\( (d) \)1.5 \mathrm{~kg}-\mathrm{m}^{2}$