Question

An ant takes $5s$ to complete one round trip along a circular path. How much time will it take for the ant to travel along the diameter of the circle and come back? Assume that the speed of the ant is constant throughout the process.

• A. $10s$
• B. $\frac{\pi }{10}s$
• C. $\frac{10}{\pi }s$
• D. $\frac{5}{\pi }s$

Answer 1

The correct option is C $\frac{10}{\pi }s$

Let the radius of the circular path be $r$.
$⟹$ the diameter of the circle $=2r$
Case 1:
The distance travelled along the circumference = $2\pi r$
Time taken, $t_1$ = $5s$
$speed=\frac{\text{distance}}{\text{time}}=\frac{2\pi r}{5}$
Case 2:
The distance travelled along the diameter = $4r$ (twice the diameter)
$Timetaken=\frac{\text{distance}}{\text{speed}}=\frac{4r}{\frac{2\pi r}{5}}$
$Timetaken=4r\times \frac{5}{2\pi r}=\frac{20}{2\pi }$
$=\frac{10}{\pi }s$ or $3.1818s$