A solid sphere $(A)$ of mass $5 m$ and a spherical shell $(B)$ of mass $m$, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of $A$ and $B$, they start rolling without slipping with an acceleration of $a_A$ and $a_B$, respectively. The ratio of $a_A$ and $a_B$ is $\_\_\_\_$ .

A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm . It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are $\_\_\_\_$ and $\_\_\_\_$ respectively.

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle $\theta_1$ and in the next 2 s it rotates through an angle $\theta_2$. The ratio $\frac{\theta_2}{\theta_1}$ is $\_\_\_\_$ .

An object of uniform density rolls up the curved path with the initial velocity $v_{\mathrm{o}}$ as shown in the figure. If the maximum height attained by an object is $\frac{7 v_0^2}{10 \mathrm{~g}}$ ( $\mathrm{g}=$ acceleration due to gravity), the object is a $\_\_\_\_$ .