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A rigid body is made of three indentical...

A rigid body is made of three indentical 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 tuns 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

A

`sqrt(g//L)`

B

`(1)/(2) sqrt(g//L)`

C

`2 sqrt(g//L)`

D

`(2)/(3)sqrt(g//L)`s

Text Solution

Verified by Experts

The correct Answer is:
D
Moment of inertia of the system of three rods about
the given axis, `I = 0 + (ml^(2))/(3) + mL^(2) = (4)/(3)mL^(2)`
As decrease in gr. `P.E. =` increase in rot. `K.E.`
`:. Mg xx (L)/(2) + mg (L) = (1)/(2)I omega^(2)`
`(3)/(2)mgL = (1)/(2) ((4)/(3)mL^(2))omega^(2)`
`omega = (3)/(2) sqrt((g)/(L))`
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