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
$2a\frac{{{s^2}}}{R}$
$2as{\left[ {1 + \frac{{{s^2}}}{{{R^2}}}} \right]^{1/2}}$
$2as$
$2a$
When a ball is freely fallen from a given height it bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce ?
A bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be
A bomb of mass $9\, kg$ explodes into two pieces of masses $3\, kg$ and $6\, kg$. The velocity of mass $3\, kg$ is $16\, m/s$. The $KE$ of mass $6\, kg$ (in joule) is
Two identical $5\,\,kg.$ blocks are moving with same speed of $2\,\,m/s$ towards each other along a frictionless horizontal surface. The two blocks collide, stick together and come to rest. Consider to two blocks as a system, the work done on the system by the external forces will be .............. $\mathrm{Joule}$
$A$ ball is projected from ground with a velocity $V$ at an angle $\theta$ to the vertical. On its path it makes an elastic collison with $a$ vertical wall and returns to ground. The total time of flight of the ball is