Q. 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
A) $\frac{M + m}{m}\sqrt{2gh}$
B) $\frac{M}{m}\sqrt{2gh}$
C) $\frac{m}{M + m}\sqrt{2gh}$
D) $\frac{m}{M}\sqrt{2gh}$
Explanation
(a) [image:6_image98.png]
By the conservation of linear momentum
Initial momentum of sphere = Final momentum of system
$mV = (m + M)v_{sys.}$ …(i)
If the system rises up to height $h$ then by the conservation of energy
$\frac{1}{2}(m + M)v_{sys.}^{2} = (m + M)gh$ …(ii)
$\Rightarrow v_{sys.} = \sqrt{2gh}$
Substituting this value in equation (i)
$V = \left( \frac{m + M}{m} \right)\sqrt{2gh}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.