A solid sphere of radius 10 cm rotates about an axis which is 15 cm from its centre. The radius of gyration is √n cm. Find n.

Solution:

Moment of inertia of solid sphere:

I_cm = (2/5)MR²

= (2/5)M(10)²

= 40M

Using Parallel Axis Theorem:

I = I_cm + Md²

= 40M + M(15)²

= 40M + 225M

= 265M

Radius of gyration:

I = Mk²

Mk² = 265M

k = √265

Therefore:

n = 265

Answer: 265