Question

There is no friction in the given situation. The carriage of mass M has constant initial velocity u along a straight horizontal track when at t = 0, it starts raining. The raindrops have a vertical velocity $u^{\prime }$ and result into addition of mass m per second to the carriage. The velocity of carriage after 7 second of start of train is :

• A. $\frac{Mu}{M+mt}$
• B. $\frac{Mu+m{u}^{\prime }}{M+mt}$
• C. $\frac{(u+u^{\prime })(M+m)}{M}$
• D. $\frac{M(u+u^{\prime })}{mt}$

Answer 1

The correct option is A $\frac{Mu}{M+mt}$

From conservation of momentum

$mu=(M+mt)V$

or $V=\frac{Mu}{M+mt}$

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