Two particles each of mass m are attached at end points of a massless rod AB of length $ℓ$ . Rod is hinged at point C as shown. Rod is released from rest from horizontal position. At the instant when rod reaches its vertical position as shown, which of the following is/are CORRECT :-

Question

TestHub · Accepted Answer

Energy conservation: A rises ℓ/4, B falls 3ℓ/4

$m g \frac{3 ℓ}{4} - m g \frac{ℓ}{4} = \frac{1}{2} [m (\frac{ℓ}{4})^{2} + m (\frac{3 ℓ}{4})^{2}] ω^{2}$

$ω^{2} = \frac{8 g}{5 ℓ}$

$v_{B} = ω \frac{3 ℓ}{4}, v_{A} = ω \frac{ℓ}{4} \Rightarrow v_{B} = 3 v_{A}$

Net torque about the hinge is zero in vertical position, so $α = 0$

Net force on B is centripetal:

$F = m ω^{2} \frac{3 ℓ}{4} = \frac{6 m g}{5}$

Hinge force has no x component

Answer: A, B, C

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Options:(select one or more)

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