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Q.
A particle of mass m moving with velocity $V_{0}$ strikes a simple pendulum of mass $m$ and sticks to it. The maximum height attained by the pendulum will be
Work, Energy and Power
Solution:
Initial momentum of particle $= mV_{0}$
Final momentum of system (particle + pendulum)
$= 2 mv$
By the law of conservation of momentum
$\Rightarrow mV_{0}=2mv$
$\Rightarrow $ Initial velocity of system $v=\frac{V_{0}}{2}$
$\therefore $ Initial $K.E.$ of the system
$=\frac{1}{2}\left(2m\right)v^{2}$
$=\frac{1}{2}\left(2m\right)\left(\frac{V_{0}}{2}\right)^{2}$
If the system rises up to height h then $P.E.=2 mgh$
By the law of conservation of energy
$=\frac{1}{2}\left(2m\right)\left(\frac{V_{0}}{2}\right)^{2}=2 mgh$
$\Rightarrow h=\frac{V^{2}_{0}}{8\,g}$
