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Q.

A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle of $30 º$ from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad $s^{- 1}$ ) will be $(g = 10 m s^{- 2})$

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a

$\sqrt{30}$

b

$\sqrt{\frac{30}{2}}$

c

$\frac{\sqrt{30}}{2}$

d

$\frac{\sqrt{20}}{3}$

answer is A.

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Detailed Solution

$m g \frac{l}{2} \sin θ = \frac{1}{2} I ω^{2} where I = \frac{m l^{2}}{3} .$

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A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle of 30º from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s-1) will be g=10ms−2