A uniform bar of length 6 a and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m moving in the same horizontal plane with speeds 2 v and v respectively, strike the bar and stick

Question

A uniform bar of length 6 a and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m moving in the same horizontal plane with speeds 2 v and v respectively, strike the bar and stick to the bar after collision. Then the angular velocity of the bar (about the centre of mass) is

TestHub · Accepted Answer

From conservation of angular momentum about point $C$

$L_{i n i t i a l (2 m)} + L_{i n i t i a l (m)} = L_{f i n a l (s y s t e m)}$

$m (2 v) (2 a) + 2 m (v) (a) = [\frac{1}{12} (8 m) {(6 a)}^{2} + m {(2 a)}^{2} + 2 m {(a)}^{2}] ω$

$6 m v a = 30 m a^{2} ω$

$ω = \frac{v}{5 a}$

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