Question

Two flies A and B revolve around a light in concentric circular path. The radius of circular path of A is twice of B. A travels with a uniform linear speed of 4 m/s while B travels with a uniform linear speed of 3 m/s. When A completes three full rounds then B would have completed

Answer 1

if radius of circular path B=s=r meter

then A has circular path twice than B=s =2r meter

speed of A=4m/s

speed of B=3m/s

time required to complete one circle for fly A  is

s=vt

t=s/v

t=2/4

t=1/2 seconds

time required to complete three circle for fly A  is

t(a)=3/2=1.5 seconds

time required to complete one circle for fly B  is

s=vt

t=s/v

t=1/3

time required to complete one circle for fly B  is

t(b)=3/3=1

as we can see that B completes one circle earlier than A and difference is

1.5-0.1=0.5

so we can conclude that when A completes one circle B will have completed 1.5 circles

and when A completes 3 circles B will have completed 4.5 circles

Answer 2

Answer: 4.5 rounds

Explanation:

The radius of path A is twice the radius of B, $r_A=2 r_B$

The uniform linear of speed of A, $v_A= 4 m/s$

The uniform linear speed of B, $v_B= 3 m/s$

The time in which A completes 3 rounds, we need to find how many rounds does B complete.

Time taken to complete 3 full rounds,

$t = 3\times \frac{2\pi r_A}{v_A}=N \times \frac{2\pi r_B}{v_B}$

$N=\frac {3\times \frac{2\pi r_A}{v_A}}{\frac{2\pi r_B}{v_B}} \Rightarrow N=\frac {3\times \frac{2\pi (2 r_B)}{4 m/s}}{\frac{2\pi r_B}{3 m/s}}=\frac {9}{2}=4.5$

Hence, when A completes three full rounds then B would have completed  four and a half rounds.