$A$ rifle bullet loses $\left(\frac{1}{20}\right)^{th}$ of its velocity in passing through a plank. Assuming that the plank exerts a constant retarding force, the least number of such planks required just to stop the bullet is .............

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
According to the observer $A$:

$A$ box of mass $3 \,kg$ moves on a horizontal frictionless table and collides with another box of mass $3 \,kg$ initially at rest on the edge of the table at height $1 \,m$. The speed of the moving box just before the collision is $4 \,m/s$. The two boxes stick together and fall from the table. The kinetic energy just before the boxes strike the floor is (Assume, acceleration due to gravity, $g=10 \,m/s^2$) (in $\,J$)

$A$ ball is released from a certain height. It loses $50\%$ of its kinetic energy on striking the ground. It will attain a height again equal to

$A$ bullet of mass $m$ moving with velocity $v_1$ strikes a wooden block of mass $M$ suspended as shown in the figure and gets embedded in it. If the block rises to a height $h$,what is the initial velocity of the bullet?

$A$ ball is held in the position shown with a string of length $L = 1 \, m$ just taut and then projected horizontally with a velocity of $u = 3 \, m/s$. If the string becomes taut again when it is vertical,the angle $\theta$ is given by ........ $^o$.