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
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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) |
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b) |
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c) |
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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