A light rod of length L is hanging from the vertical smooth wall of a vehicle moving with acceleration 3 g along the horizontal plane having a small mass attached at its one end and is free to rotate about an axis passing through the other end. The minimum velocity given to the mass at its equilibrium position with respect to the vehicle so that it can complete vertical circular motion is

Question

A light rod of length L is hanging from the vertical smooth wall of a vehicle moving with acceleration 3 g along the horizontal plane having a small mass attached at its one end and is free to rotate about an axis passing through the other end. The minimum velocity given to the mass at its equilibrium position with respect to the vehicle so that it can complete vertical circular motion is, 5 g L, 4 g L, 8 g L, None of these

MARKS App · Accepted Answer

The effective acceleration due to gravity in the reference frame of the vehicle is g e f f = g 2 + 3 g 2 = 2 g The angle made by g e f f with the verticle is θ = tan - 1 3 g g = 60 ° At the lowest point (shown in the figure), let the speed is v , then 1 2 m v 2 = m 2 g 2 L ⇒ v = 8 g L

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