A container of mass $m$ is pulled by a constant force in which a second block of same mass $m$ is placed connected to the wall by a mass-less spring of constant $k$ . Initially the spring is in its natural length. Velocity of the container at the instant when compression in spring is maximum for the first time
$\pi F\sqrt {\frac{1}{{2km}}} $
$\frac{{\pi F}}{2}\sqrt {\frac{1}{{2km}}} $
$\pi F\sqrt {\frac{1}{{km}}} $
$\frac{{\pi F}}{2}\sqrt {\frac{1}{{km}}} $
The work done by a force $\vec F = \left( { - 6{x^3}\hat i} \right)\,N$ in displacing a particle from $x = 4\,m$ to $x = -2\,m$ is ............... $\mathrm{J}$
A body of mass $m$ moving with velocity $v$ collides head on with another body of mass $2\, m$ which is initially at rest. The ratio of $K.E.$ of the colliding body before and after collision will be
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 vertical spring with force constant $K$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is
Ball $A$ moving at $12\ m/s$ collides elastically with $B$ at rest as shown. If both balls have the same mass, what is the final velocity of ball $A$ ? .................. $m/s$