Question

A vehicle having a mass of 500 kg is moving with a speed of 10 m/s. Sand is dropped into it at the rate of 10 kg/min. The force needed to keep the vehicle moving with a uniform speed will be - 
1. \(\dfrac{5}{3} N\)
2. \(\dfrac{3}{5} N\)
3. \(\dfrac{1}{5} N\)
4. 5 N

Answer 1

Correct Answer - Option 1 : \(\dfrac{5}{3} N\)

Ans: Option: 1)

Concept:

Newtons Second law of motion: 

It states that the rate of change of momentum is directly proportional to the impressed force.

\(F= \frac{\mathrm{d} P}{\mathrm{d} t}\)

Where P = momentum and is the product of mass and velocity.

Calculation: 

Given:

Mass of vehicle = 500 kg

speed (v) = 10 m/s

Change of mass in a truck i.e, \(\frac{\mathrm{d} m}{\mathrm{d} t}\) = 10 kg/min = 10 kg/60sec =  \(\frac{1}{6}\) kg/sec

Using Newtons second law of motion,

\(F= \frac{\mathrm{d} P}{\mathrm{d} t}\)  here P = mv

\(F= v\frac{\mathrm{d} m}{\mathrm{d} t}\)  here velocity is constant .

Putting values in the above equation,

F = 10 × \(\frac 16\)

F = \(\frac 53\) N

The correct answer is option 1)