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# A sphere of mass m moving with velocity v enters, a hanging bag of sand and stops. If the mass of bag is M and it is raised by height h, then the velocity of sphere was

$(a)\;\frac{M+m}{m} \sqrt {2gh} \quad (b)\;\frac{M}{m} \sqrt {2gh} \quad (c)\;\frac{m}{M+m} \sqrt {2gh} \quad (d)\;\frac{m}{M} \sqrt {2gh}$

Answer: $\large\frac{M+m}{m}$$\sqrt {2gh} Per law of conservation of linear momentum mV=(m+M)v_{\large system}-----(1) Per law of conservation of energy \large\frac{1}{2}$$(m+M)v_{\large system}^2=(m+M)gh$
$\Rightarrow v_{\large system}=\sqrt {2gh}$