Given, Mass of ball P and Q be mP and mQ where, mp=m and mQ=2m Initial velocity of P and Q is uP,uQ i.e. up=v and uQ=0 and final velocity of P and Q is vP,vQ. Coefficient of restitution, e=1∕3 As we know that e=
vP−vQ
uQ−uP
∴
1
3
=
vP−vQ
0−v
⇒
1
3
=
vP−vQ
−v
⇒vP−vQ=−
v
3
. . . (i) By using law of conservation of momentum, mPuP+mQuQ=mPvP+mQvQ ⇒mv+2m.0=mvP+2mvQ ⇒v=vP+2vQ. . . (ii) Now, subtracting Eq. (i) from Eq. (ii), as +v=+vP+2vQ −v∕3=+vP−vQ +− 4v∕3=3vQ⇒vQ=4v∕9 Substituting in Eq. (ii), we get vP=v−2vQ =v−2⋅
