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Grade 12AIPMT

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?

sayantani bardhan

9 Years agoGrade 12

1 Answer

Eshan

8 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 length $l$ is $v$ , 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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