iii. In a certain unit the radius of gyration of a uniform disc about its central and transverse axis is K. Its radius of gyration about a tangent in its plane (in the same unit) must be a. √5 2 b. √2 5 c. √2 d.
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the moment of inertia ,I, by the parallel axis theorem is
I= I[c] +Ml^2 , here
I[c] =[1/4] M.r^2 , and since l=r Ml^2 = M.r^2 then.
I= [1/4]M.r^2 + Mr^2 = [5/4]M.r^2 is the moment of inertia perpendicular to the plane of the disc and tangent to the edge.
I= M k^2 where k is the radius of gyration
Mk^2= [5/4]M .r^2
k^2 =[5/4].r^2
k =[ sq rt 5].r/2
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