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} $

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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} $



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