A boy and a girl are riding on a merry-go-round that is turning. The boy is twice as far as the girl from the merry-go-rounds center. If the boy and girl are of equal mass, which statement is true about the boys moment of inertia with respect to the axis of rotation?

I (boy) = 4 I (girl)

Explanation:

Moment of inertia is given by - the product of the mass and the square of the radius.

Hence,

I = mr²

Where, I = moment of inertia,

m = mass of the object

r = radius,

hence, from the question,

The mass of girl and boy is equal, i. e.,

m (boy) = m (girl)

and,

r (boy) = 2 * r (girl)

By using the above equation, the Moment of inertia is as follow -

I (girl) = m (girl) r² (girl)

I (boy) = m (boy) r² (boy)

I (boy) = m (boy) (2 * r (girl)) ²

I (boy) = m (boy) 4 r² (girl)

both the mass are equal,

I (boy) = 4 I (girl)