Question

An open carriage in a goods train is moving with a uniform velocity of 10 m/s. If the train adds water with zero velocity at the rate of 5 kg/s, then the additional force applied by the engine to maintain the same velocity of the train is:
A. 0.5 N
B. 2.0 N
C. 50 N
D. 25 N

Answer 1

Hint: In this question we have been given that water is added by moving t 10 m/s at the rate of 5 kg/s. we have been asked to calculate the additional force applied by the train to maintain same velocity after water is added. Now, from Newton’s second law we know that force is given as rate of change of momentum. Therefore, we shall use Newton’s second law to calculate our answer.

Formula used:
 \[F=\dfrac{dP}{dt}\]
Where,
F is the force applied
P is momentum and t is time

Complete step by step solution:
Now, it is given that water is added at zero velocity to the carriage moving at speed of 10 m/s. we know that when water is added to the carriage, the total mass of the system will increase. Therefore, due to increase in mass the momentum of the system will change.
We know from Newton’s second law that,
\[F=\dfrac{dP}{dt}\] …………….. (1)
We also know that,
\[P=mv\] …………… (2)
From (1) and (2)
We get,
\[F=\dfrac{d(mv)}{dt}\] ……………….. (3)
We have been given that water is added at the rate of 5 kg/s
So,
\[\dfrac{dm}{dt}=5kg/s\]………….. (4)
From (3)
We get,
\[F=\dfrac{dm}{dt}\times v\]
After substituting from (4) and given,
We get,
\[F=5\times 10\]
Therefore,
\[F=50N\]

So, the correct answer is “Option C”.

Note: Momentum is the product of mass and velocity of a body. If the direction of momentum vector and velocity is the same, the momentum is known as linear momentum. By Newton’s second law, rate of change of momentum is the force acting on the body. If the mass of the system is constant, the force is given as the product of mass and acceleration or rate of change of velocity of the body.