8-1MCQ Bonnie sits on the outer rim of ... [FREE SOLUTION]

Chapter 8: 8-1MCQ (page 198)

Bonnie sits on the outer rim of a merry-go-round, and Jill sits midway between the centre and the rim. The merry-go-round makes one complete revolution every 2 seconds. Jill’s linear velocity is:

(a) the same as Bonnie’s.

(b) twice Bonnie’s.

(c) half of Bonnie’s.

(d) one-quarter of Bonnie’s.

(e) four times Bonnie’s.

Short Answer

Expert verified

The correct answer is option (c) half of Bonnie’s.

Step by step solution

Given data

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

Understanding linear velocity

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.

Determine the velocity of Jill

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.