A rod of negligible mass and length ℓ is pivoted at its centre. A particle of mass m is fixed to its left end and another particle of mass 2m is fixed to the right end. If the system is released from

Question

A rod of negligible mass and length ℓ is pivoted at its centre. A particle of mass m is fixed to its left end and another particle of mass 2m is fixed to the right end. If the system is released from rest and after sometime becomes vertical, the speed v of the two masses and the angular speed at that instant is :-

TestHub · Accepted Answer

Energy conservation: loss of PE = gain of KE

Mass 2m falls ℓ/2 and mass m rises ℓ/2:

$\frac{2 m g ℓ}{2} - \frac{m g ℓ}{2} = \frac{1}{2} [\frac{m ℓ ^{2}}{4} + \frac{2 m ℓ ^{2}}{4}] ω^{2}$

$\frac{m g ℓ}{2} = \frac{3 m ℓ ^{2}}{8} ω^{2}$

$ω = \frac{4 g}{3 ℓ}$

$v = ω \frac{ℓ}{2} = \frac{g ℓ}{3}$

Answer: A

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