Question

$M$ is mass, $R$ is radius of a solid cylinder and its length is $3R$. The moment of inertia of this solid cylinder about an axis perpendicular to the length of cylinder and passing through its centre is:

• A. $M{R}^2$
• B. $\frac{M{R}^2}{3}$
• C. $\frac{M{R}^2}{4}$
• D. $\frac{3M{R}^2}{4}$

Answer 1

The correct option is A $M{R}^2$

The MI of the solid cylinder about an axis perpendicular to the length of cylinder of height $H$ with radius $R$, and passing through its centre is $I=M(3R^2+H^2)/12$

here $H=3R$

So, $I=M(3R^2+(3R{)}^2)/12=12M{R}^2/12=M{R}^2$