A sphere of mass $m$, moving with velocity $V$, enters a hanging bag of sand and stops. If the mass of the bag is $M$ and it is raised by height $h$, then the velocity of the sphere was
$\frac{{M + m}}{m}\sqrt {2gh} $
$\frac{M}{m}\sqrt {2gh} $
$\frac{m}{{M + m}}\sqrt {2gh} $
$\frac{m}{M}\sqrt {2gh} $
A small ball falling vertically downward with constant velocity $4m/s$ strikes elastically $a$ massive inclined cart moving with velocity $4m/s$ horizontally as shown. The velocity of the rebound of the ball is
A person trying to lose weight (dieter) lifts a $10\; kg$ mass, one thousand times, to a hetght of $0.5\; m$ each time. Assume that the potential energy lost each time she lowers the mass is dissipated.
$(a)$ How much work does she do against the gravitational force?
$(b)$ Fat supplies $3.8 \times 10^{7} \;J$ of energy per kilogram which is converted to mechanical energy with a $20 \%$ efficiency rate. How much fat will the dieter use up?
A body falls towards earth in air. Will its total mechanical energy be conserved during the fall ? Justify.
From a stationary tank of mass $125000$ pound a small shell of mass $25$ pound is fired with a muzzle velocity of $1000\, ft/sec$. The tank recoils with a velocity of ............ $\mathrm{ft/sec}$
A particle of mass $0.1 \,kg$ is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at $x = 0$, its velocity at $x = 12\,m$ is .......... $m/s$