Question

Two buses a and b are moving around concentric circular paths of radii ra and rb. If the two buses complete circular paths in the same time , the ratio of the linear speeds is

Answer 1

Answer:

$S_A:S_B=r_a:r_b$

Explanation:

Formula used:

Linear speed

= Linear distance / time taken

Let t be the taken by the buses A and B to complete the circuilar path

For bus A:

Distance travelled in in time t

=Length of the cicular path having radius $r_a$

$=2\:\pi\:r_a$

Then,

Linear speed, $S_A=\frac{2\:\pi\:r_a}{t}$

For bus B:

Distance travelled in in time t

=Length of the cicular path having radius $r_b$

$=2\:\pi\:r_b$

Then,

Linear speed, $S_B=\frac{2\:\pi\:r_b}{t}$

Now,

$S_A:S_B=\frac{2\:\pi\:r_a}{t}:\frac{2\:\pi\:r_b}{t}$

$S_A:S_B=2\:\pi\:r_a:2\:\pi\:r_b$

$S_A:S_B=r_a:r_b$