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A weightless rigid rod of length 2l with a load at the end is hinged at point A to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible thread of length l, fixed at its midpoint. The load receives a small momentum in the direction perpendicular to the plane of the figure. The time period T of small oscillation of the system is.

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a

$2 π \sqrt{\frac{2 l}{g}}$

b

$2 π \sqrt{\frac{4 l}{g}}$

c

$2 π \sqrt{\frac{l}{g}}$

d

$2 π \sqrt{\frac{3 l}{g}}$

answer is B.

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Detailed Solution

Small oscillation occurs relative to stationary axis passing through AB. DC perpendicular to line passing through AB becomes length of equivalent pendulum.
Question Image
$T = 2 π \sqrt{\frac{L \sin θ}{g \cos θ}} = 2 π \sqrt{\frac{L \tan θ}{g}} T = 2 π \sqrt{\frac{2 l}{g}}$

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