Question

If two objects move in circular path of radii in the ratio of 1:3 and take same time to complete the circle, what is the ratio of their speeds?​

Answer 1

Let the radius be x and 3x.

For smaller circle :-

Radius = x

Time taken = t (say)

Circumference = Distance travelled

Hence,

Circumference =

$= 2\pi x$

$\rule{200}{2}$

For bigger circle :-

Radius = 3x

Time taken = t (say)

Circumference = Distance travelled

Thus,

Circumference =

$= 6\pi x$

$\rule{200}{2}$

The speed will be :-

$= \frac{2\pi x}{t}$

$= \frac{6\pi x}{t}$

$\rule{200}{2}$

The ratio of their speeds will be as follows :-

$= \frac{2\pi x}{6\pi x} \\ \\ \\ = \frac{2}{6} \\ \\ \\ = \frac{1}{3} \\ \\ \\ = 1:3$

$\rule{200}{2}$

Answer 2

Solution :-

Let the radius of circular path be r and 3r respectively.

Let the speed of first and second object be v¹ and v² respectively.

The length of the first track = 2πr

Time taken by the 1st object t = 2πr/v¹

The length of the second track = 6πr

Time taken by the 2nd object t = 6πr/v²

Time taken by both object are same

→ 2πr/v¹ = 6πr/v²

→ v¹ : v² = 1 : 3