AIPMT 2010 Physics and Chemistry Paper

Here, m1=m,m2=2m
u1=2m∕s,u2=0
coefficient of restitution, e=0.5
Let v1 and v2 be their respective velocities after collision.
Applying the law of conservation of linear momentum, we get
m1u1+m2u2=m1v1+m2v2
∴‌‌m×2+2m×0=m×v1+2m×v2
or 2m=mv1+2mv2
or 2=(v1+2v2)...(i)
By definition of coefficient of restitution,
e=‌

v2−v1

u1−u2

or ‌‌e(u1−u2)=v2−v1
0.5(2−0)=v2−v1....(ii)
1=v2−v1
Solving equations (i) and (ii), we get
v1=0m/s,v2=1m/s