\[\begin {array} {1 1} (a)\;\frac{2J}{p}-1 & \quad (b)\;\frac{J}{p}+1 \\ (c)\;\frac{J}{p}-1 & \quad (d)\;\frac{J}{4p}-1 \end {array}\]

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Impulse on A =-Impulse on B

Impulse = change in momentum

Let $u_1$ be the initial velocity of A

$p= mu_1$

After collision let $v_1$ and $v_2$ be the velocities of A and B in the same direction.

$J= mv_2$ ---- (1)

$-J=mv_1-mu_1$

$J=mu_1-mv_1$

$J= p-mv_1$ ----(2)

$2J= p+m(v_2-v_1)$

$2J-p= m(v_2-v_1)$

$\large\frac{v_2-v_1}{u_1}$$=e$

$\qquad= \large\frac{2J-p}{p}$

$\qquad= \large\frac{2J}{p}$$-1$

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