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Two particles A,B are moving on two conc...

Two particles A,B are moving on two concentric circles of radii `R_1` and `R_2` with equal angular speed `omega`. At`t=0`,their positions and direction of motion are shown in the figure. The relative velocity `vecV_a-vecV_b` at `t=pi//2omega` is given by :

A

`omega (R_(1) - R_(2)) hat(i)`

B

`omega(R_(1) + R_(2)) hat(i)`

C

`-omega(R_(1) + R_(2))hat(i)`

D

`omega(R_(2) - R_(1))hat(i)`

Text Solution

Verified by Experts

The correct Answer is:
D
At `t = (pi)/(2 omega), theta = omega t = (pi)/(2)`. Hence the position of A and B would be
`vec(V)_(A) = R_(1) omega(-hat(i))`
`vec(V)_(B) = R_(2)omega(-hat(i))`
`vec(V)_(A) - vec(V)_(B) = (R_(1)omega - R_(2) omega)(-hat(i))`
Or `vec(V)_(A) - vec(V)_(B) = (R_(2) - R_(1)) omega (hat(i))`
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