A uniform rod of length $ 2.0 \mathrm{~m} $ is suspended through its endpoint about which it performs small angular oscillations in the vertical plane. Its time period is nearly

Question

A uniform rod of length $ 2.0 \mathrm{~m} $ is suspended through its endpoint about which it performs small angular oscillations in the vertical plane. Its time period is nearly, $ 1.6 \mathrm{~s} $, $ 1.8 \mathrm{~s} $, $ 2.0 \mathrm{~s} $, $ 2.3 \mathrm{~s} $

MARKS App · Accepted Answer

It is a physical pendulum, and its time period T = 2 π I m g x Here l = moment of inertia of the pendulum about point of suspension I = M L 2 12 + M L 2 4 = M L 2 3 and x = distance of point of suspension from its COM. x = L 2 ⇒ T = 2 π M L 2 3 m g L 2 = 2 π 2 L 3 g ⇒ T = 2 π 2 × 2 3 × 10 = 2. 3 sec .

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