$A$ 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 .............

$A$ large block of wood of mass $M = 5.99 \, kg$ is hanging from two long massless cords. $A$ bullet of mass $m = 10 \, g$ is fired into the block and gets embedded in it. The (block $+$ bullet) then swing upwards,their centre of mass rising a vertical distance $h = 9.8 \, cm$ before the (block $+$ bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (Take $g = 9.8 \, ms^{-2}$) (in $m/s$)

$A$ bob $B$ of mass $m$ at rest is hanging vertically from the ceiling via a massless string of length $10 \text{ m}$. $A$ point mass $A$ of mass $m$ travelling horizontally with speed $10 \text{ ms}^{-1}$ hits bob $B$ elastically. The bob $B$ rises $h$ meters after the collision. Taking the acceleration due to gravity $g = 10 \text{ ms}^{-2}$ and neglecting the size of the bob, the value of $h$ is:

$A$ body of mass $(4m)$ is lying in the $x-y$ plane at rest. It suddenly explodes into three pieces. Two pieces,each of mass $(m)$,move perpendicular to each other with equal speeds $(v)$. The total kinetic energy generated due to the explosion is ................. $mv^2$.

$A$ machine which is $70 \%$ efficient raises a $10 \,kg$ body through a certain distance and spends $100 \,J$ energy. The body is then released. On reaching the ground, the kinetic energy of the body will be

$A$ lift of mass $2000 \ kg$ starts from rest in the basement and moves to the fourth floor,which is at a height of $25 \ m$. As it passes the fourth floor,its speed is $3 \ ms^{-1}$. There is a constant frictional force of $500 \ N$ acting on it. Calculate the work done by the lift's motor in $kJ$.