Question

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

Answer 1

The moment of inertia of the system about one rod as axis `I=(mL^(2))/3+mL^(2), I=4/3 mL^(2)`
Potential energy decreases for `B` and `C`

`(mgL)/2+mgL=3/2mgL`
By conservation of mechanical energy, the loss 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=3/2sqrt(g/L)`