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 R√x, 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 A2 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=R√2 On comparing with R√x, x=2