$A$ bullet moving with a velocity of $100\, m/s$ can just penetrate two planks of equal thickness. The number of such planks penetrated by the same bullet,when the velocity is doubled,will be

$A$ wooden block of mass $M$ is suspended by a string. $A$ bullet of mass $m$ passes through the block with velocity $v$ and emerges with a velocity $v/2$ in the same direction. To what height will the block rise?

$A$ bullet of mass $m$ moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$,the initial velocity of the bullet will be

$A$ 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 ................. $mv^2$.

Particle $A$ of mass $m_{1}$ moving with velocity $(\sqrt{3} \hat{i} + \hat{j}) \, m/s$ collides with another particle $B$ of mass $m_{2}$ which is at rest initially. Let $\vec{V}_{1}$ and $\vec{V}_{2}$ be the velocities of particles $A$ and $B$ after collision,respectively. If $m_{1} = 2m_{2}$ and after collision $\vec{V}_{1} = (\hat{i} + \sqrt{3} \hat{j}) \, m/s$,the angle between $\vec{V}_{1}$ and $\vec{V}_{2}$ is $......^{\circ}$.

$A$ person of mass $60 \, kg$ wants to lose $5 \, kg$ by going up and down a $10 \, m$ high stairs. Assume he burns twice as much fat while going up than coming down. If $1 \, kg$ of fat is burnt on expending $7000 \, kcal$,how many times must he go up and down to reduce his weight by $5 \, kg$?