Question

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?

Answer 1

Answer:

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)