A shell of mass $m$ moving with velocity $v$ suddenly breakes into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be
$v$
$\frac{5v}{4}$
$\frac{4v}{5}$
$\frac{v}{5}$
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
The diagram to the right shows the velocity-time graph for two masses $R$ and $S$ that collided elastically. Which of the following statements is true?
$(I)$ $R$ and $S$ moved in the same direction after the collision.
$(II)$ Kinetic energy of the system $(R$ & $S)$ is minimum at $t = 2$ milli sec.
$(III)$ The mass of $R$ was greater than mass of $S.$
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
In the non-relativistic regime, if the momentum, is increased by $100\%$, the percentage increase in kinetic energy is
A ball is dropped from height $h$ on a plane. If the coefficient of restitution of the plane is $e$ and if ball hits ground two times, the height upto which it reaches after two jumps, will be