Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be √x cm. The value of x i $s ______$ .

Question

Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be √x cm. The value of x i s ______ .

G1 Physics · Accepted Answer

For a solid sphere about its centre, I c m I_cm I c ​ m = (2/5)MR². The axis PQ is 10 cm from the centre. By parallel-axis theorem, I P Q I_PQ I P ​ Q = (2/5)MR² + M(10 cm)² = M[(2/5)(5²) + 100] = 110M cm². Since I = Mk², k² = 110 cm², so x = 110.