A light stick of length ℓ rests with its one end against the smooth wall and other end against the smooth horizontal floor as shown in the figure. The bug starts at rest from point B and moves such th

Question

A light stick of length ℓ rests with its one end against the smooth wall and other end against the smooth horizontal floor as shown in the figure. The bug starts at rest from point B and moves such that the stick always remains at rest, a p ​ is the magnitude of acceleration of bug of mass m , which depends upon its distance of x from the top end of the stick. Choose the CORRECT option(s) :

TestHub · Accepted Answer

Consider the bug at point P at any time t, moving with speed v along the stick, so

$L = m v h = m v t sin θ cos θ \Rightarrow Angular momentum of bug about point O \Rightarrow τ = \frac{d L}{d t} = (m ℓ sin θ cos θ) \frac{d v}{d t} \Rightarrow m g (ℓ - x) cos θ = (m ℓ sin θ cos θ) \frac{d v}{d t} \Rightarrow \frac{d v}{d t} = \frac{g}{sin θ} (1 - \frac{x}{ℓ}) \Rightarrow \frac{d v}{d t} + \frac{g}{ℓ sin θ} x = \frac{g}{sin θ} Equation of S H M with mean position at point A \Rightarrow T = 2 π \frac{ℓ sin θ}{g} Time required = \frac{T}{4} = \frac{π}{2} \frac{ℓ sin θ}{g}$

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Options:(select one or more)

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