# 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)

## Question ID - 100198 :- 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)

3537

(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

Next Question :

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)