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Question:

A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed ω, as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v with respect to the rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system remains ω throughout. The magnitude of the torque |τ| on the system about O, as a function of time is best represented by which plot?

Solution:

L = [mr²]ω
L = [mv²t²]ω
L = mv²ωt²
τ = ΔL/Δt = 2mv²ωt (directly differentiate the eq. given above)
τ ∝ t
Therefore, straight line passes through (0,0)