$A$ small ball $B$ of mass $m$ is suspended with a light inelastic string of length $L$ from a block $A$ of the same mass $m$,which can move on a smooth horizontal surface as shown in the figure. The ball is displaced by an angle $\theta$ from the equilibrium position and then released. The tension in the string when it is vertical is:

$A$ person with a machine gun can fire $50 \ g$ bullets with a velocity of $240 \ m/s$. $A$ $60 \ kg$ tiger moves towards him with a velocity of $12 \ m/s$. In order to stop the tiger in its track,the number of bullets the person must fire towards the tiger is:

$A$ balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$). How much mass should be removed from it so that it starts moving up with an acceleration $a$?

$A$ person used force $(F)$,shown in the figure,to move a load with a constant velocity on a given surface. Identify the correct surface profile.

The figure shows an arrangement of a rod of length $l$ and mass $M$ and a bead of mass $m$ attached to a weightless string passing over a frictionless pulley. At $t = 0$,the bead is level with the lower end of the rod. The bead slides down the string with considerable friction and is opposite to the other end of the rod after $T$ seconds. Assuming friction between the bead and the string to be constant throughout,the frictional force is:

In the figures $(i), (ii)$ and $(iii)$ shown, the objects $A, B$ and $C$ have the same mass $m$. The string, spring, and pulley are massless. Object $C$ strikes object $B$ with velocity $u$ in each case and sticks to it. Find the ratio of the velocity of $B$ in case $(i)$ to $(ii)$ to $(iii)$.