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Question

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

A
v02
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B
v02
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C
v04
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D
2v0
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Solution

## The correct option is D √2v0By conservation of linear momentum mv0+0=mv1+mv2 v0=v1+v2 ..........(1) 32[12mv20]=12mv21+12mv22 32v20=v21+v22⋯⋯⋯⋅(2) Solving equation (1) and (2) v1=v02(1+√2) v2=v02(1−√2) ¯¯¯vrel=¯¯¯v1−¯¯¯v2 v02[1+√2−1+√2] =v02×2√2 =√2v0

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