Two circular loops P and Q of radii ' r ' and ' nr ' are made respectively from a uniform wire. Moment of inertia of loop Q about its axis is four times that of loop P about its axis. The value of ' $n$ ' is

A solid sphere of mass ' $m$ ', radius ' $R$ ', having moment of inertia about an axis passing through center of mass as 'I' is recast into a disc of thickness ' $t$ ' whose moment of inertia about an axis passing through the rim (edge) \& perpendicular to plane remains 'I'. Then the radius of disc is

An inclined plane makes an angle of $30^{\circ}$ with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration ( $\mathrm{g}=$ acceleration due to gravity, $\sin 30^{\circ}=0.5$ )

An annular ring has mass 10 kg and inner and outer radii are 10 m and 5 m respectively. Its moment of inertia about an axis passing through its centre and perpendicular to its plane is