A) \[\frac{M+m}{m}\sqrt{2gh}\]
B) \[\frac{M}{m}\sqrt{2gh}\]
C) \[\frac{m}{M+m}\sqrt{2gh}\]
D) \[\frac{m}{M}\sqrt{2gh}\]
Correct Answer: A
Solution :
By the conservation of linear momentum Initial momentum of sphere = Final momentum of system \[mV=(m+M){{v}_{\text{sys}\text{.}}}\] ?(i) If the system rises up to height h then by the conservation of energy \[\frac{1}{2}(m+M)v_{\text{sys}\text{.}}^{\text{2}}=(m+M)gh\] ?(ii) Þ \[{{v}_{\text{sys}\text{.}}}=\sqrt{2gh}\] Substituting this value in equation (i) \[V=\left( \frac{m+M}{m} \right)\ \sqrt{2gh}\]You need to login to perform this action.
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