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If rho is the density of its material, t...

If `rho` is the density of its material, then its rotational K.E. is given by

A

`(AL^(3)rho omega^(2))/(24)`

B

`(AL^(3)rho omega^(2))/(6)`

C

`(AL^(2)rho omega^(2))/(24)`

D

`(AL^(3)rho^(2)omega)/(24)`

Text Solution

Verified by Experts

The correct Answer is:
A
The M.I. of the rod about the given axis is `I=(ML^(2))/(12)`
Mass of the rod `=Vxx rho=A xx Lxxrho`
`therefore" "I=((Alrho).L^(2))/(12)=(AL^(3)rho)/(12)`
`therefore" Rotational K.E."=(1)/(2)Iomega^(2)`
`=(1)/(2)(AL^(3)rho)/(12)omega^(2)=(AL^(3)rho omega^(2))/(24)`
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