A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is √n cm. The value of n i s ________.

Question

G1 Physics · Accepted Answer

For a solid sphere, the moment of inertia about an axis through its centre is I(CM) = (2/5)MR². For a parallel axis at distance d from the centre, I = I(CM)+Md². If k is the radius of gyration about the given axis, I = Mk². Therefore, k² = (2/5)R²+d². Given, R = 10 cm, d = 15 cm. Hence, k² = (2/5)(10)²+(15)² = 40+225 = 265 cm². Thus, k = √265 cm. Since the question writes k = √n cm, n = 265. Hence the answer is 265.