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Two particles, of masses M and 2M, movin...

Two particles, of masses M and 2M, moving as shown, with speeds of `10m//s` and `5m//s`, collide elastically at the origin.After the collision, they move along the indicated directions with speeds `v_1` and `v_2` , respectively.The values of `v_1` and `v_2` are nearly :

A

6.5 m/s and 6.3 m/s

B

3.2 m/s and 6.3 m/s

C

3.2 m/s and 12.6 m/s

D

6.5 m/s and 3.2 m/s

Text Solution

Verified by Experts

The correct Answer is:
A
From conservation of momentum
Along x-direction.
`M(10) cos 30^(@) +(2M)(5)cos 45^(@) =(2M).v_(1)cos30^(@) + M.v_(2)cos45^(@)`
`rArr sqrt(3)v_(1) + v_(2)/sqrt(2) = 5sqrt(3) + 5sqrt(2)`………..(1)
Along y-direction.
`(2M) xx (5)sin 45^(@) -M(10)sin 30^(@) =(2M)v_(1)sin30^(@)-My_(2)sin45^(@) rArr v_(1) -v_(2)/sqrt(2) = 5sqrt(2) -5`............(2)
Solving (1) and (2)
`v_(1) =6.5 m//s` , `v_(2) = 6.3 m//s`
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