$A$ heavy rod of weight $W$ is held in a horizontal position by two men at its ends. If one man suddenly lets go,what force will the other man feel?

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

$A$ cubical block of side $a = 30\,cm$ is moving with velocity $v = 2\,m/s$ on a smooth horizontal surface. The surface has a small bump at a point $O$ as shown in the figure. The angular velocity (in $rad/s$) of the block immediately after it hits the bump is:

$A$ metal sphere of radius $r$ and specific heat $S$ is rotated about an axis passing through its centre at a speed of $n$ rotations per second. It is suddenly stopped and $50 \%$ of its energy is used in increasing its temperature. Then,the rise in temperature of the sphere is

Two equal masses each of mass $M$ are joined by a massless rod of length $L$. Now an impulse $J = MV$ is given to one of the masses,making an angle of $30^{\circ}$ with the length of the rod. The angular velocity of the rod just after imparting the impulse is:

$A$ bar of mass $M=1.00 \ kg$ and length $L=0.20 \ m$ is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. $A$ small mass $m=0.10 \ kg$ is moving on the same horizontal surface with $5.00 \ m \ s^{-1}$ speed on a path perpendicular to the bar. It hits the bar at a distance $L/2$ from the pivoted end and returns back on the same path with speed $v$. After this elastic collision,the bar rotates with an angular velocity $\omega$. Which of the following statements is correct?