Work, Energy, Power & Collision / कार्य, ऊर्जा और शक्ति
JEE Main & Advanced
Physics
Work, Energy, Power & Collision / कार्य, ऊर्जा और शक्ति
Question Bank
Conservation of Energy and Momentum
question_answer
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]
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) \[V=\left( \frac{m+M}{m} \right)\ \sqrt{2gh}\]