Question

A child rolls a ball on a level floor 3.5 m to another child. If the ball makes 12.0 revolutions, what is its diameter?

Short answer

The diameter of the ball is \(9.28 \times {10^{ - 2}}\;{\rm{m}}\).

Step-by-step solution

Relationship between the circumference of the circle and distance covered by an object 

When an object having a circular cross-section revolves, the distance traveled by a point on its periphery in one revolution is similar to its circumference.

Thus, the distance that the ball covers in each revolution will be equal to its circumference.

Given information

Given data:

The distance covered by the ball is\(l = 3.5\;{\rm{m}}\).

The number of revolutions is \(N = 12.0\;{\rm{rev}}\).

Calculate the diameter of the ball 

The expression for the circumference of the ball is as follows:

\(c = \pi D\)

Here,\(D\)is the diameter of the ball.

Now, the diameter of the ball can be calculated by using the following expression.

\(\begin{aligned}{c}c = \frac{l}{N}\\\pi D = \frac{l}{N}\\D = \frac{l}{{\pi N}}\end{aligned}\)

Substitute the values in the above expression.

\(\begin{aligned}{l}D = \frac{{\left( {3.5\;{\rm{m}}} \right)}}{{\pi \left( {12.0\;{\rm{rev}}} \right)}}\\D = 9.28 \times {10^{ - 2}}\;{\rm{m}}\end{aligned}\)

Thus, the diameter of the ball is \(9.28 \times {10^{ - 2}}\;{\rm{m}}\).