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 = sqrt(3) R`
C. `L = R//sqrt(3)`
D. `L = 0`

Answer

B

Explanation

(b) Given `I_1 = I_2`
`rArr (1)/(2) MR^2 = (mL^2)/(12) + (mR^2)/(4)`
solve to get `L = sqrt(3) R`.
.