A wooden block of mass $M$ is suspended by a cord and is at rest. A bullet of mass $m,$ moving with a velocity $v$ passes through the block and comes out with a velocity $v/2$ in the same direction. If there is no loss in kinetic energy, then upto what height the block will rise
$m^2v^2/2M^2g$
$m^2v^2/8M^2g$
$mv^2/4Mg$
$mv^2/2Mg$
A mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass initially at rest. After collision the first mass moves with velocity $\frac{v}{\sqrt 3}$ in a direction perpendicular to its initial direction of motion. The speed of second mass after collision is
A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is
A body of mass $m$ is moving in a circle of radius $r$ with a constant speed $v$. The force on the body is $\frac{mv^2}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle
Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by
A $15\, g$ ball is shot from a spring gun whose spring has a force constant of $600\, N\, m$. The spring is compressed by $3\, cm$. The greatest possible velocity of the ball for this compression is ............. $\mathrm{m}/ \mathrm{s}$ $(g = 10\, m/s^2$)