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Physics - Circular Motion Question with Solution | TestHub

PhysicsCircular MotionKinematicsMedium2 minQB

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A semicircular wire of radius r is supported in its own vertical plane by a hinge at O and smooth peg P as shown. If peg starts from O and moves with constant speed v along horizontal axis through O. The angular speed of wire is

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Answer:

Solution:

Chord $OP = 2 r sin θ = v t$ , so $sin θ = \frac{v t}{2 r}$ .

Differentiating: $cos θ \frac{d θ}{d t} = \frac{v}{2 r}$ .

$ω = \frac{d θ}{d t} = \frac{v}{2 r 1 - \frac{v ^{2} t ^{2}}{4 r ^{2}}} = \frac{v}{4 r ^{2} - v ^{2} t ^{2}}$ - (A)

Stream:JEESubject:PhysicsTopic:Circular MotionSubtopic:Kinematics

⏱ 2mℹ️ Source: QB

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