Three balls and of masses 2 kg, 4 kg and 8 kg, respectively, move along the same straight line and in the same direction, with velocities 4 m/s, 1 m/s and 3/4 m/s. If collides with and subsequently collides with , find the velocity of ball and ball after collision, taking the coefficient of restitution as unity
a) 

b) 

c) 

d) 
Three balls and of masses 2 kg, 4 kg and 8 kg, respectively, move along the same straight line and in the same direction, with velocities 4 m/s, 1 m/s and 3/4 m/s. If collides with and subsequently collides with , find the velocity of ball and ball after collision, taking the coefficient of restitution as unity
a) 

b) 

c) 

d) 
(d)
First consider the collision of balls and Let the velocities of these two balls after their collision be and
Momentum after impact = Momentum before impact
(i)
Relative velocity after impact relative velocity before impact
(ii)
Subtracting Eq. (ii) from Eq. (i). we get
m/s
Substituting in Eq. (ii), we get
Hence, after the collision ball is brought to rest, while ball will move with a velocity of 3 m/s. Now consider the collision of balls and . Let the velocities of these balls after collision be and respectively
Total momentum after impact = Total momentum before impact
(iii)
Relative velocity after impact = relative velocity before impact
(iv)
Subtracting Eq.(iv) from Eq.(iii), we get
m/s
The system in fig. is released from rest from the position shown. After blocks have moved distance collar is removed and block and continue to move. The speed of just before it strikes the ground is
a) 
b) 
c) 
d) 
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