A ball of mass $m$ is dropped from a heigh $h$ on a platform fixed at the top of a vertical spring, as shown in figure. The platform is depressed by a distance $x.$ Then the spring constant is
$\frac{{mg}}{{(h + x)}}$
$\frac{{mg}}{{(h + 2x)}}$
$\frac{{2mg(h + x)}}{{{x^2}}}$
$\frac{{mg}}{{(2h + x)}}$
The variation of force $F$ acting on a body moving along $x$-axis varies with its position $(x)$ as shown in figure The body is in stable equilibrium state at
A ball moving with velocity $2\, m/s$ collides head on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $m/s$) after collision will be
A particle is moved from $(0, 0)$ to $(a, a)$ under a force $\vec F = (3\hat i + 4\hat j)$ from two paths. Path $1$ is $OP$ and path $2$ is $OQP$. Let $W_1$ and $W_2$ be the work done by this force in these two paths respectively. Then
A body is dropped from a height $h$ . If it acquires a momentum $p$ just before striking the ground, then the mass of the body is
The spacecraft of mass $M$ moves with velocity $V$ in free space at first, then it explodes breaking into two pieces. If after explosion a piece of mass $m$ comes to rest, the other piece of space craft will have a velocity