A bullet of mass $m$ strikes a block of mass $M$ connected to a light spring of stiffness $k,$ with a speed $v_0.$ If the bullet gets embedded in the block then, the maximum compression in the spring is
${\left( {\frac{{{m^2}v_0^2}}{{(M + m)k}}} \right)^{1/2}}$
${\left( {\frac{{Mmv_0^2}}{{2(M + m)k}}} \right)^{1/2}}$
${\left( {\frac{{mv_0^2}}{{2(M + m)k}}} \right)^{1/2}}$
${\left( {\frac{{Mv^2}}{{(M + m)k}}} \right)^{1/2}}$
A spring with spring constant $k $ is extended from $x = 0$to$x = {x_1}$. The work done will be
An elastic string of unstretched length $L$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. The work done in the second stretching is
The potential energy of a long spring when stretched by $2\,cm$ is $U$. If the spring is stretched by $8\,cm$, potential energy stored in it will be $.......\,U$
$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block To an observer
$A$, the work done by the normal reaction $N$ between the block and the spring on the block is
Define spring constant and write its unit.