# A rod of length 50cm is provided at one end. It is raised such that if makes an angle of $30^{\circ}$ 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)Option 1)$\frac{\sqrt{20}}{3}$Option 2)  $\sqrt{\frac{30}{2}}$Option 3)$\sqrt{30}$Option 4)$\frac{\sqrt{30}}{2}$

Kinetic energy of rotation -

$K=\frac{1}{2}Iw^{2}$

- wherein

$I$ = moment of inertia about axis of rotation

$w$ = angular velocity

Work done by gravity from intial to final point

$W=mg\frac{l}{2}\sin 30^{\circ}$

$=\frac{mgl}{4}$........................................(1)

By work energy theorem

$W=\frac{1}{2}I\omega ^{2}$

$=\frac{1}{2}{\frac{mL^{3}}{3}}\omega ^{2}$..........................(2)

from (1) and (2)

$\omega =\sqrt{30}\: rad/sec$

Option 1)

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

Option 2)

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

Option 3)

$\sqrt{30}$

Option 4)

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

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