Question

An cyclist completes one round of a circular track of radius R is 20 seconds. How many rotations it will take at the end of 2min 20sec:-
1. 5 rotations
2. 4 rotations
3. 3 rotations
4. 7 rotations

Answer 1

Correct Answer - Option 4 : 7 rotations

CONCEPT:

• The total distance covered in one rotation on a circular path is 

2 π R.

• speed is inversely proportional to the time

\(S \propto \frac{1}{T}\)

• to remove the proportionality we add D as a constant.

\( S = \frac{D}{T}\)

EXPLANATION:

• circumference of circle = distance covered in one rotation
• speed of the cyclist is given by 

\(s = \frac{2π R}{20}\)

\(s = \frac{π R}{10}\)

• The total distance it will cover is 

\(D = S \times T\)

\(D = \frac{π R}{10} \times 140\)

\(D = 14 π R\)

• The number of rotations is given by = (Total distance covered / Distance covered in one rotation).

\(=\frac{14 π R}{2 π R} = 7\)

• The total number of rotations is 7. Hence option 4 is the answer.