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 4 times that of loop $P$ about its axis. The value of $n$ is

Three spheres, each of mass ' $m$ ' and radius ' $r$ ' are placed as shown in figure. Consider an axis $\mathrm{YY}^{\prime}$, which is touching two spheres and passing through the diameter of third sphere. The moment of inertia of the system consisting of these three spheres about $\mathrm{YY}^{\prime}$ axis is

A wheel initially at rest, begins to rotate about its axis with constant angular acceleration. If it rotates through an angle $\theta_1$ in first 2 s and a further angle $\theta_2$ in the next 2 s , the ratio $\theta_1: \theta_2$ is

A solid sphere rolling without friction on a horizontal surface with a constant speed of $2 \mathrm{~m} / \mathrm{s}$, rolls up on an inclined ramp which is inclined at $30^{\circ}$. The maximum distance travelled by the sphere on the inclined ramp is (acceleration due to gravity $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sin 30^{\circ}=\frac{1}{2}$ )