Question

There is a circular swimming pool. There is a bob at the centre of the pool at a distance of $\frac{50}{\pi }$ m from the pool’s wall. Shyam is standing next to the

wall and holding a thread whose other end is connected to the heavy stationary bob at the centre. Holding the thread Shyam now moves along the wall for 20

seconds and the angle between the initial and final positions of the thread is ${12}^{\circ }$. What is Shyam’s speed in metres/minute?

Answer 1

The distance between bob at centre and wall is nothing but radius of circular pool because radius is distance between centre of circle and boundary

(circumference). The path travelled by Shyam is along the wall of a circular boundary. So it is an arc. The angle subtended by arc is the angle between initial

and final positions of Ram which is ${12}^{\circ }$. Hence we can find arc length by formula-

Arc length =$\frac{\theta }{360}$ $\times$ 2$\pi$r

Here r is radius r = $\frac{50}{\pi }$ m

Angle subtended by arc θ = ${12}^{\circ }$Substituting these values in the formula we get- Arc length = $\frac{10}{3}$ cm

Speed = Distance/Time

Distance = Arc length = $\frac{10}{3}$ cm

Time = 20 seconds = $\frac{1}{3}$ minute

Speed = Distance/time = $\frac{\frac{10}{3}}{\frac{1}{3}}$ = 10 m/min