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

Two particles of masses M and 2M, moving as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated diretions with speeds `v_(1)` and `v_(2)` respectively. The value of `v_(1)` and `v_(2)` are nearly:

A

6.5m/s and 3.2m/s

B

3.2 m/s and 6.3m/s

C

6.5m/s and 6.3m/s

D

3.2 m/s and 12.6m/s

Text Solution

Verified by Experts

The correct Answer is:
C
Using momentum conservation In X- direction `m xx 10cos 30^(@) + 2m (5)/(sqrt2) = (mv_(2))/(sqrt2) 2mv_(1) (sqrt3)/(2)`
`5 sqrt6+10= v_(2)+ sqrt6 V_(1)` ...(i)
In Y- direction
`2m (5)/(sqrt2)- m (10)/(2)= (2mv_(1))/(2)- (mv_(2))/(sqrt2)`
`10- 5 sqrt2 = sqrt2 V_(1)-V_(2)` ...(ii)
Using (i) and (ii)
`V_(1)= 6.516 m//s`
`V_(2)= 6.3 m//s`
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