Four smooth steel balls of equal mass at rest are free to move along a straight line without friction. The first ball is given a velocity of $0.4\, m/s$. It collides head on with the second elastically, the second one similarly with the third and so on. The velocity of the last ball is .............. $\mathrm{m}/ \mathrm{s}$
$0.4$
$0.2$
$0.1$
$0.05$
When the momentum of a body increases by $100\%$, its $KE$ increases by .............. $\%$
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 small block of mass $m$ slides along a smooth frictional track as shown in the figure. If it starts from rest at $P$ , velocity of block at point $Q$ is
A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to:
A spring of force constant $K$ is first stretched by distance a from its natural length and then further by distance $b$. The work done in stretching the part $b$ is .............