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In a collinear collision, a particle wit...

In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is :

A

`sqrt3 v_(0)`

B

`(v_(0))/(sqrt2)`

C

`(v_(0))/(sqrt3)`

D

`sqrt2 v_(0)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `(1)/(2) mv_(1)^(2) + (1)/(2) mv_(2)^(2)= 1.5 ((1)/(2) mv_(0)^(2))`
`rArr v_(1)^(2)+ v_(2)^(2)= 1.5 v_(0)^(2)` ...(i)
From law of conservation of momentum `mv_(1) + mv_(2)= mv_(0)`
`rArr v_(1) + v_(2)= v_(0)` ...(ii)
From (i) and (ii)
`v_(1) + (v_(0)- v_(1))^(2)= 1.5 v_(0)^(2)`
`rArr 2v_(1)^(2)- 2v_(0)v_(1)- 0.5 v_(0)^(2)= 0`
Now, Relative velocity `= {v_(2)-v_(1)]` = difference of Roots `=sqrt2v_(0)`
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