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option B
let the mass of two ball be M1 and M2
velocity is given u and v
momentum before impact
= m1u1+ m2u2
momentum after impact= m1v1 + m2v2
kinetic energy before impact
= m1u(1)^2/2 +m2u(2)^2/2
kinetic energy after impact
= m1(v1)^2/2 + m2v(2)^2/2
according to the principle of conservation of energy
kinetic energy before impact = kinetic energy after impact
on relation we get
v1 = {(m1 - m2)u1 + m2u2}/(m1+m2)
v2 = {(m2 - m1)u2 + m1u1}/m1 + m2
since
Md^2r/dt^2-------(1
and
M a(c)--------(2
where a(C) is acceleration of the centre of mass
using ----(1 and (2 relation
so
v1 - v2 = u1 - u2
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