Question

Radius of gyration of a body about an axis$\left(I_A\right)$ is $5\text{m}$. Perpendicular distance of $\left(I_A\right)$ from center of mass of body is $3\text{m}$. Find its radius of gyration about an axis$\left(I_B\right)$ which is parallel to $\left(I_A\right)$ and also passing through center of mass of body.

• A. $4\text{m}$
• B. $5\text{m}$
• C. $3\text{m}$
• D. $6\text{m}$

Answer 1

The correct option is A $4\text{m}$

Let the mass of the body$=m$
Let radius of gyration about a parallel axis $I_B$ through its center of mass = $K_B$
Given:
radius of gyration of body about an axis $I_A$ at a distance $3\text{m}$ from its center of mass is $K_A=5\text{m}$

Applying parallel axis theorem,
$I_A=I_B+m{d}^2$ [here $d=3\text{m}$]
$m{K}_A^2=m{k}_B^2+m{d}^2$
$K_B=\sqrt{K_A^2-d^2}$
$=\sqrt{5^2-3^2}$
$=4\text{m}$