Sand is deposited at a uniform rate of $20\ kg/s$ and with negligible kinetic energy on an empty conveyor belt moving horizontally at a constant speed of $10$ meters per minute. Find the force required to maintain constant velocity of the conveyor belt.

A particle $A$ is projected vertically upwards. Another particle $B$ is projected at an angle of $45^{\circ}$. Both reach the same height. The ratio of the initial kinetic energy of $A$ to that of $B$ is

A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by $1\,m/s$ so as to have same K.E. as that of the boy. The original speed of the man will be

Two particles having masses $4\, g$ and $16\, g$ respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is $n : 2 .$ The value of $n$ will be ...... .

The kinetic energy of a body of mass $3 \,kg$ and momentum $2 \,N-s$ is

Two masses of $1 \,gm$ and $4 \,gm$ are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is