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 :

Options

A. `(v_0)/(2)`
B. `(v_0)/(sqrt2)`
C. `(v_0)/(4)`
D. `sqrt(2)v_0`

Answer

D

Explanation

It is given that final total kinetic energy has increased, so some internal energy of the system must have been converted into kinetic energy.
`1/2 mv_1^2 + 1/2 mv_2^2 = 1.5(1/2 mv_0^2) implies v_1^2 + v_2^2 = 1.5 v_0^2 " "……(i)`
Since, there is no external force, momentum can be conserved
`mv_1 + mv_2 = mv_0 implies v_1 + v_2 = v_0 " "......(ii)`
From (i) & (ii)
`v_1 + (v_0 - v_1)^2 = 1.5 v_0^2 , " "2v_1^2 - 2 v_0v_1 - 0.5 v_0^2 = 0`
Relative velocity `=|v_2 - v_1| =` Difference of roots `=(sqrtD)/(a) = sqrt(2)v_0`.