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Question

Radius of gyration of a uniform disc about a line perpendicular to the plane of disc is equal to its radius R. If the distance of the line from the center is Rx, find the value of x.

A
2
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B
4
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C
1
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D
8
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Solution

The correct option is A 2
Let the mass of disc is M
Let the distance of the line from the center is d.
Moment of inertia about the line (I)
Radius of gyration about the line (K)
Applying parallel axes theorem,
I=Icom+Md2
We know,
K=IM
So, K=Icom+Md2M
Given: K=R
R=  MR22+Md2M

R=R22+d2
Squaring on both sides,
R2=R22+d2
d=R2
On comparing with Rx, x=2

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