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Question: In the shown system friction is meaningless. The car­riage of mass M has constant initial velocity u...

In the shown system friction is meaningless. The car­riage of mass M has constant initial velocity u along a straight horizontal track when at t = 0, it starts raining. The rain drops have a vertical velocity u' and result into addition of mass m per second to the carriage. The velocity of carriage after T second of start of rain is

A

MuM+mt\frac{Mu}{M + mt}

B

Mu+mu′M+mt\frac{Mu + mu'}{M + mt}

C

(u+u′)(M+m)M\frac{(u + u')(M + m)}{M}

D

M(u+u′)mt\frac{M(u + u')}{mt}

Answer

MuM+mt\frac{Mu}{M + mt}

Explanation

Solution

From conservation of momentum

Mu = (M + mt)V

or V = MuM+Mt\frac{Mu}{M + Mt}

vertical down pour of rain does not effect the horizontal motion of carriage but addition of mass of water to mass of the carriage changes the velocity.