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 is
Q. 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 is ____.

Correct Answer: 265

Explanation

For a solid sphere, the moment of inertia about an axis passing through its centre is:

Icm = 2/5 MR²

Here, radius R = 10 cm.

The given axis is at a distance d = 15 cm from the centre, so we apply the parallel axis theorem:

I = Icm + Md²

I = M(2/5 × 10² + 15²)

I = M(40 + 225)

I = 265M

The radius of gyration k is defined by:

I = Mk²

Mk² = 265M

k = √265 cm

Hence, the value of n is:

265

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