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A rod of length 50 cm is pivoted at one end. It is raised so that it makes 30° with the horizontal and released from rest. Its angular speed when it passes through the horizontal is (take g=10 m/s²)

Asked in JEE Main 9th Jan 2nd Shift 2019 · Rotational energy and released bodies

Answer: (3) √30

Step-by-step solution

The CM (at /L2) drops by /L2 sin 30°=/L4 as the rod goes from 30° to horizontal.

Energy: mg/L4=1/2((mL²)/3)ω²⇒ ω²=(3g)/(2L)=(3(10))/(2(0.5))=30.

ω=√30 rad/s.

Why the other options are wrong

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