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A rigid body is made of three identical ...

A rigid body is made of three identical thin rods, each with length fastened together in the form. of letter `H`. The body is free to rotate about a horizontal axis that runs along the length of one of the arms of `H`. The body is allowed to fall from rest from a position in which the plane of the `H` is horizontal. What is the angular speed of the body when the plane of `H` is vertical?

Text Solution

Verified by Experts

The moment of inertia of the system about the axis is `I=(4)/(3)mL^(2)`. By conservation of mechanical energy the lose in PE of body is equal to the gain in rotational KE.
`:.(3)/(2)mgL=(1)/(2)((4)/(3)mL^(2))omega^(2)`
on solving `omega=(3)/(2)sqrt((g)/(L))`
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