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}

Answers (1)
A admin

 

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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