Work equal to $25\,J$ is done on a mass of $2\,kg$ to set it in motion. If the whole of it is used to increase the kinetic energy,then the velocity acquired by the mass is ............ $m/s$.

State and establish the principle of conservation of mechanical energy.

$A$ particle slides from the top of a smooth hemispherical surface of radius $R$ which is fixed on a horizontal surface. If it separates from the hemisphere at a height $h$ from the horizontal surface,then the speed of the particle is

$A$ body dropped from height $H$ reaches the ground with a speed of $1.1 \sqrt{gH}$. Calculate the work done by air friction in terms of $mgH$.

$A$ $30 \, g$ bullet initially travelling at $120 \, m/s$ penetrates $12 \, cm$ into a wooden block. The average resistance force exerted by the wooden block is ........... $N$.

$A$ particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that: