Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# The radius of gyration of a body about an axis at a distance of $12 \mathrm{cm}$ from its centre of mass is $13 \mathrm{cm} .$ Then the radius of gyration of the body about a parallel axis through its C.O.M is (in $\mathrm{cm}$ ):(A) 25(B) 625(C) 2.5(D) 5

Last updated date: 20th Jun 2024
Total views: 404.7k
Views today: 6.04k
Verified
404.7k+ views
Hint
We know the radius of gyration or gyradius of a body about an axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated. The distance from an axis at which the mass of a body may be assumed to be concentrated and at which the moment of inertia will be equal to the moment of inertia of the actual mass about the axis, equal to the square root of the quotient of the moment of inertia and the mass. Based on this concept you have to solve this question.

$\Rightarrow \mathrm{K}_{1}=13 \mathrm{cm}$
$\Rightarrow \mathrm{I}_{\text {com }}+\mathrm{m}(12)^{2}=\mathrm{m}(13)^{2}$
$\Rightarrow \mathrm{I}_{\mathrm{com}}=25 \mathrm{m}$
Now $\mathrm{K}_{2}$ is radius of gyration about $\mathrm{COM}$. $\mathrm{mK}_{2}^{2}=25 \mathrm{m}$
$\Rightarrow \mathrm{K}_{2}=5 \mathrm{cm}$