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
$\frac{1}{2}m{v^2} \times \frac{m}{{(m + M)}}$
$\frac{1}{2}m{v^2} \times \frac{M}{{(m + M)}}$
$\frac{1}{2}m{v^2} \times \frac{M+m}{{(M)}}$
$\frac{1}{2}m{v^2} \times \frac{2m}{{( M+m)}}$
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 bag of sand of mass $M$ is suspended by a string. A bullet of mass $m$ is fired at it with velocity $v$ and gets embedded into it. The loss of kinetic energy in this process is
A body of mass $M$ is dropped from a height $h$ on a sand floor. If the body penetrates $x\,\,cm$ into the sand, the average resistance offered by the sand of the body is
A long spring, when stretched by a distance $x,$ has the potential energy $u.$ On increasing the stretching to $nx.$ The potential energy of the spring will be
A body of mass $m$ is moving in a circle of radius $r$ with a constant speed $u$. The force on the body is $mv^2/r$ 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?