Question

The moment of inertia of a solid cylinder about its natural axis is $I$. If its moment of inertia about an axis perpendicular to natural axis of cylinder and passing through one end of cylinder is $\frac{19}{6}I$ 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

The correct option is A $1:2$

The moment of inertia of a solid cylinder about its natural axis is $I=m{r}^2$ ..(1)

Moment of inertia about an axis perpendicular to natural axis of cylinder and passing through one end of cylinder is $I_1=\frac{19I}{6}=\frac{m{r}^2}{4}+\frac{m{l}^2}{3}$...(2)

From 1 and 2 , we get $4r^2=l^2\Rightarrow \frac{r}{l}=1:2$