Q.

A and B are moving in two circular orbits with angular velocity 2ω and ω respectively. Their positions are as shown at t = 0 . Find the time when they will meet for the first time.

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a

Never meet

b

π2ω

c

πω

d

3π2ω

answer is D.

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Detailed Solution

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For same sense ( let say both anticlockwise) :

Ball A-

First time A reaches to common point , t1=2π2ω=πω

Second time A reaches to common point , t2=πω+πω=2πω

So, the time series is πω , 2πω, 3πω, 4πω.....

Ball B :

First time B reaches to common point , t1=3π2ω=1.5πω

Second time B reaches to common point , t2=1.5πω+2πω=3.5πω

So, the time series is 1.5πω , 3.5πω, 5.5πω, 7.5πω.....

There is no common time when A and B meet.

 

For opposite sense ( let say A anticlockwise ad B clockwise) :

Ball A-

First time A reaches to common point , t1=2π2ω=πω

Second time A reaches to common point , t2=πω+πω=2πω

So, the time series is πω , 2πω, 3πω, 4πω.....

Ball B :

First time B reaches to common point , t1=π2ω=0.5πω

Second time B reaches to common point , t2=0.5πω+2πω=2.5πω

So, the time series is 0.5πω , 2.5πω, 4.5πω, 6.5πω.....

Again, there is no common time when A and B meet.

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