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Two point masses 1 and 2 move with unifo...

Two point masses 1 and 2 move with uniform velocities `vec(v)_(1)` and `vec(v)_(2)`, respectively. Their initial position vectors are `vec(r )_(1)` and `vec(r )_(2)`, respectively. Which of the following should be satisfied for the collision of the point masses?

A

`(vec(r )_(1)-vec(r )_(2))/(|vec(r )_(2)-vec(r )_(1)|)=(vec(v)_(2)-vec(v)_(1))/(|vec(v)_(2)-vec(v)_(1)|)`

B

`(vec(r )_(2)-vec(r )_(1))/(|vec(r )_(2)-vec(r )_(1)|)=(vec(v)_(2)-vec(v)_(1))/(|vec(v)_(2)-vec(v)_(1)|)`

C

`(vec(r)_(2)-vec(r )_(1))/(|vec(r )_(2)+vec(r )_(1)|)=(vec(v)_(2)-vec(v)_(1))/(|vec(v)_(2)+vec(v)_(1)|)`

D

`(vec(r)_(2)-vec(r )_(1))/(|vec(r )_(2)+vec(r )_(1)|)=(vec(v)_(2)-vec(v)_(1))/(|vec(v)_(2)+vec(v)_(1)|)`

Text Solution

Verified by Experts

The correct Answer is:
B
For collision,

`vec(r )_(1)+vec(v)_(1)t=vec(r )_(2)+vec(v)_(2)t`
or `vec(r )_(1)-vec(r )_(2)=(vec(v)_(2)-vec(v)_(1))t`
Equating unit vectors, we get
`(vec(r )_(1)-vec(r )_(2))/(|vec(r )_(2)-vec(r )_(1)|)=(vec(v)_(2)-vec(v)_(1))/(|vec(v)_(2)-vec(v)_(1)|)`
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