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A meter scale is suspended freely from one of its ends. Its another end is given a horizontal velocity v such that it completes one revolution in vertical circle. The value of v is?

A meter scale is suspended freely from one of its ends. Its another end is given a horizontal velocity v such that it completes one revolution in vertical circle. The value of v is?

Grade:12

1 Answers

Eshan
askIITians Faculty 2095 Points
4 years ago
Dear student,

The meter scale could be at rest when reaching at the top to just complete the circle, unlike the case of ball tied to a string.
So the whole rotational kinetic energy of the ruler would go into the gain in gravitational potential energy.

If the horizontal speed of end of the ruler of lengthlisv, angular velocity of the same will be\omega=\dfrac{v}{l}.

From conservation of energy,

\dfrac{1}{2}I\omega^2=mg(\dfrac{l}{2}+\dfrac{l}{2})
\implies \dfrac{1}{2}(m\dfrac{l^2}{3})\omega^2=mg(\dfrac{l}{2}+\dfrac{l}{2})
\implies v=\omega l=\sqrt{6gl}

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