Work Energy And Power Question 57
Question: 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 [MP PET 1997]
Options:
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} $
Show Answer
Answer:
Correct Answer: A
Solution:
By the conservation of linear momentum Initial momentum of sphere = Final momentum of system
$ mV=(m+M){v _{sys\text{.}}} $ -(i)
If the system rises up to height h then by the conservation of energy
$ \frac{1}{2}(m+M)v _{sys\text{.}}^{2}=(m+M)gh $ -(ii)
therefore $ {v _{sys\text{.}}}=\sqrt{2gh} $
Substituting this value in equation (i) $ V=( \frac{m+M}{m} )\ \sqrt{2gh} $
