Question

The moment of inertia of a solid cylinder about its natural axis is I. if its moment of inertia about an axis $\perp$ to natural axis of cylinder and passing through, one end of cylinder is 191/6 then the ratio of radius of cylinder and its length is

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

Answer 1

Answer: (A)

$I=\frac{M{R}^2}{2}$
$I_1=\frac{19I}{6}=\frac{M{L}^2}{3}+\frac{M{R}^2}{4}$
$\Rightarrow$ $\frac{19}{6}\left(\frac{M{R}^2}{2}\right)=\frac{M{L}^2}{3}+\frac{M{R}^2}{4}$
$\Rightarrow$ $\frac{R}{L}=\frac{1}{2}$