Question

The radius of gyration of a body is 18 cm when it is rotating about an axis passing through center of mass of body. If radius of gyration of same body is 30 cm about a parallel axis to first axis then, perpendicular distance between two parallel axes is:

• A. 12 cm
• B. 16 cm
• C. 24 cm
• D. 36 cm

Answer 1

Answer: (C)

24 cm

Given :$I_{CM}=M{K}^2$ where 'K' is the radius of gyration of the body.

$K=18cm$

Moment of Inertia around an axis parallel to the axis passing through center of mass is

$I=I_{CM}+M{x}^2$

'x' is the perpendicular distance of the axis from the CM axis.
The radius of gyration for this new Moment of Inertia is 30 cm

$M{d}^2=M{K}^2+M{x}^2$

$x^2=d^2-K^2$

$x^2={30}^2-{18}^2$

$x=24cm$