A uniform cylinder has radius `R` and length `L`. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is `(mR^(2))/2` is equal to moment of inertia of the same cylinder about an axis passing through its centre and normal to its length, then

Options

A. L= R
B. `L= sqrt3R`
C. `L= (R)/(sqrt3)`
D. `L= sqrt((3)/(2))R`

Answer

B

Explanation

`I_(1)= (MR^(2))/(2), I_(2) = (ML^(2))/(12) + (MR^(2))/(4)`
Since, `I_(1)= I_(2)`
`(MR^(2))/(2)= (ML^(2))/(12) + (MR^(2))/(4)`

`rArr (MR^(2))/(4)= (ML^(2))/(12) rArr L= sqrt3R`