$A$ particle of mass $m$ is released from $a$ height $H$ on $a$ smooth curved surface which ends into a vertical loop of radius $R$, as shown The minimum value of $H$ required so that the particle makes a complete vertical circle is given by
$5 \,R$
$4\, R$
$2.5\, R$
$2\, R$
The kinetic energy $K$ of a particle moving along a circle of radius $R$ depends upon the distance $s$ as $K = as^2$. The force acting on the particle is
Two blocks $A$ and $B$ of masses $1\,\,kg$ and $2\,\,kg$ are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to stretch the spring and then released. The ratio of $K.E.s$ of both the blocks is
A particle of mass $M$ starting from rest undergoes uniform acceleration. If the speed acquired in time $T$ is $V$, then power delivered to the particle in time $T$ is
A particle of mass $7\, kg$ moving at $5\, m/s$ is acted upon by a variable force opposite to its initial direction of motion. The variation of force $F$ is shown as a function of time $t$.
A batsman hits a sixer and the ball touches the ground outside the cricket ground. Which of the following graph describes the variation of the cricket ball's vertical velocity $v$ with time between the time ${t_1}$ as it hits the bat and time $t_2$ when it touches the ground