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
Text Solution
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By the conservation of linear momentum
Initial momentum of sphere
= Final momentum of system
$mV = \left(m + M\right) v_{\mathrm{sys}.}$ …(i)
If the system rises up to height h then by the conservation of energy
$\frac{1}{2}(m+M)v_{\text{sys.}}^{2} = (m+M)gh$ …(ii)
⇒ ⇒ $v_{\text{sys.}} = \sqrt{2gh}$
Substituting this value in equation (i)
$V = \left(\frac{m+M}{m}\right) \sqrt{2gh}$
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