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2019 Q1: A particle of mass m is moving with a velocity v. It collides with another stationary particle of mass m and gets stuck to it. The speed of the combined mass is:
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(A) $\frac{v}{2}$
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(B) $\frac{v}{3}$
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(C) $\frac{v}{4}$
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(D) $\frac{2v}{3}$
The answer is (D).
In a perfectly inelastic collision, the two objects stick together and move with the same velocity after the collision. The total momentum of the system before the collision is mv, and the total momentum of the system after the collision is (m + m)v. Therefore, the velocity of the combined mass after the collision is v = mv/(m + m) = 2v/3.
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2018 Q2: A particle of mass m is moving with a constant velocity v. It collides with another stationary particle of mass m and gets stuck to it. The kinetic energy of the system after collision is:
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(A) $\frac{mv^2}{
