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Question
Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of 2 m s−1 and 1 m s−1, respectively. They collide and after the collision, the first object moves at a velocity of 1.67 m s−1. Determine the velocity of the second object.
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Solution
Mass of one of the objects, m1 = 100 g = 0.1 kg
Mass of the other object, m2 = 200 g = 0.2 kg
Velocity of m1 before collision, v1 = 2 m/s
Velocity of m2 before collision, v2 = 1 m/s
Velocity of m1 after collision, v3 = 1.67 m/s
Velocity of m2 after collision = v4
According to the law of conservation of momentum:-
Total momentum before collision = Total momentum after collision
∴ m1v1 + m2v2 = m1v3 + m2v4
(0.1)2 + (0.2)1 = (0.1)1.67 + (0.2)v4
0.4 = 0.167 + 0.2v4
∴ v4 = 1.165 m/s
Hence, the velocity of the second object becomes 1.165 m/s after the collision.
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