91Ó°ÊÓ

The time required to complete the revolution is \(t = 2\;{\rm{s}}\).

In this problem, one of the misconceptions is that if Jill and Bonnie consume equal time to complete the merry-go-round, their linear velocities will be equivalent.

Bonnie is sitting on the outer edge of the merry-go-round, whereas Jill is sitting midway between the center and the rim. So, the distance traveled by Bonnie will be more compared to the distance covered by Jill.

The relation of the linear velocity of Bonnie is:

\({v_{\rm{B}}} = \omega r\)

Here, r is the radius of the ride and \(\omega \) is the angular velocity.

The relation of the linear velocity of Jill is:

\(\begin{aligned}{l}{v_{\rm{J}}} = \omega \left( {\frac{r}{2}} \right)\\{v_{\rm{J}}} = \left( {\frac{1}{2}} \right)\omega r\\{v_{\rm{J}}} = \left( {\frac{1}{2}} \right){v_{\rm{B}}}\end{aligned}\)

Thus, option (c) is the correct answer.