Question

$I$ is the moment of inertia of a solid cylinder about an axis parallel to the length of cylinder and passing through its centre. If moment of inertia of same solid cylinder about an axis perpendicular to length of cylinder and passing through its centre is $2I$, the ratio of radius of cylinder and its length is:

• A. $1:2$
• B. $1:3$
• C. $1:4$
• D. $1:6$

Answer 1

The correct option is B $1:3$

The moment of inertia of a solid cylinder about an axis parallel to the length of cylinder $I=M{R}^2/2$..(1)

Moment of inertia of same solid cylinder about an axis perpendicular to length of cylinder and passing through its center is $I_1=2I=M{R}^2/4+M{L}^2/12$..(2) (directly using perpendicular axis theorem)

On directly taking the ratio and solving the equation 1 and 2, we get $R/L=1/3$