A man is standing on a cart of mass double the mass of man. Initially cart is at rest. Now man jumps horizontally with relative velocity $'u'$ with respect to cart. Then work done by internal forces of the man during the process of jumping will be :

A light spring of length $20\, cm$ and force constant $2\, kg/cm$ is placed vertically on a table. A small block of mass $1\, kg$. falls on it. The length $h$ from the surface of the table at which the ball will have the maximum velocity is ............... $\mathrm{cm}$

A body at rest breaks up into $3$ parts. If $2$ parts having equal masses fly off perpendicularly each after with a velocity of $12m/s$, then the velocity of the third part which has $3$ times mass of each part is

$A$ small sphere is moving at $a$ constant speed in $a$ vertical circle. Below is a list of quantities that could be used to describe some aspect of the motion of the sphere.

$I$ - kinetic energy

$II$- gravitational potential energy

$III$ - momentum

Which of these quantities will change as this sphere moves around the circle?

$A$ projectile of mass $"m"$ is projected from ground with a speed of $50 \,m/s$ at an angle of $53^o$ with the horizontal. It breaks up into two equal parts at the highest point of the trajectory. One particle coming to rest immediately after the explosion. The distance between the pieces of the projectile when they reach the ground are:

A mass $M$ moving with a certain speed $V$ collides elastically with another stationary mass $m$. After the collision, the masses $M$ and $m$ move with speeds $V^{\prime}$ and $v$, respectively. All motion is in one dimension. Then,