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

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Using the parallel axis theorem for radius of gyration:

k^2 = k_{cm}^2 + d^2

where

k_{cm}

is the radius of gyration about the center of mass and

d

is the distance from the center.
For a solid sphere:

I_{center} = \frac{2}{5}MR^2

, so

k_{cm}^2 = \frac{2}{5}R^2

With

R = 10

cm and

d = 15

cm:

k^2 = \frac{2}{5}(10)^2 + (15)^2 = 40 + 225 = 265

Since

k = \sqrt{n}

, we have

n = 265

.

A solid sphere of radius 10 cm is rotating about an axis which is...

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