QNEET-2023-Ph-254: NEET 2023 Physics - Class 11 NEET-2023-Ph-254 Solution: The ratio of radius of gyration of a solid sphere of mass M and …

To solve this problem, we need to find the ratio of the radius of gyration for a solid sphere (K_) to the radius of gyration for a thin hollow sphere (K_) of the same mass M and radius R. The moment of inertia (I) of a solid sphere about its own axis is given by : I s o l i d = 2 5 M R 2 The radius of gyration (K) is related to the moment of inertia (I) and mass (M) by the formula : I = M K 2 So for the solid sphere, we can find K_ using : K 1 2 = I s o l i d M = 2 5 R 2 K 1 = R 2 5 Now, for a thin hollow sphere, the moment of inertia about its axis is given by : I h o l l o w = 2 3 M R 2 We can find K_ using : K 2 2 = I h o l l o w M = 2 3 R 2 K 2 = R 2 3 Now, we need to find the ratio K_ : K_ : K 1 K 2 = R 2 5 R 2 3 The R terms cancel out, and we are left with : K 1 K 2 = 2 5 2 3 Simplify by taking the square root of the fraction : K 1 K 2 = 2 3 5 2 Now, the square root of 2 terms cancel out, giving us : K 1 K 2 = 3 5