A body of mass $m\, kg$ is rotating in a vertical circle at the end of a string of length $r$ metre. The difference in the kinetic energy at the top and the bottom of the circle is

A particle is moving eastwards with velocity of $5\,m/s$. In $10 \,sec$ the velocity changes to $5 \,m/s$ northwards. The average acceleration in this time is

For a particle in uniform circular motion, the acceleration $\overrightarrow{ a }$ at any point $P ( R , \theta)$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive $x\,-$axis and $v$ is uniform speed)

A ball is projected with velocity $V_0$ at an angle of elevation $30^o $ . Mark the correct statement

A body of mass $1 \,kg$ is projected from ground at an angle $30^{\circ}$ with horizontal on a level ground at a speed $50 \,m / s$. The magnitude of change in momentum of the body during its flight is ....... $kg ms ^{-1}$ $\left(g=10 \,m / s ^2\right)$

Two cars of masses $m_1$ & $m_2$ are moving along the circular paths of radius $r_1$ & $r_2$ respectively. Their speeds are such that they complete one round in same time. The ratio of angular speeds of two cars is