A cart is moving with a velocity 20m/s. Sand is being dropped into the cart at the rate of 50 kg/min. The force required to move the cart with constant velocity will be :-

Options

A. 50 N
B. 30.33N
C. 26.45N
D. 16.66N

Answer

To solve the problem, we need to determine the force required to keep the cart moving at a constant velocity while sand is being dropped into it. We will use the concept of momentum and the rate of change of mass.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Velocity of the cart, \( v = 20 \, \text{m/s} \)
- Rate at which sand is being dropped into the cart, \( \frac{dm}{dt} = 50 \, \text{kg/min} \)

2. **Convert the Rate of Mass Flow:**
- We need to convert the mass flow rate from kg/min to kg/s:
\[ \frac{dm}{dt} = 50 \, \text{kg/min} \times \frac{1 \, \text{min}}{60 \, \text{s}} = \frac{50}{60} \, \text{kg/s} = \frac{5}{6} \, \text{kg/s} \approx 8.33 \, \text{kg/s} \]

3. **Use the Formula for Force:**
- The force required to keep the cart moving at a constant velocity while the mass is changing can be expressed as:
\[ F = v \frac{dm}{dt} \]
- Substituting the values we have:
\[ F = 20 \, \text{m/s} \times \frac{5}{6} \, \text{kg/s} \]

4. **Calculate the Force:**
- Now we perform the multiplication:
\[ F = 20 \times \frac{5}{6} = \frac{100}{6} \, \text{N} \approx 16.67 \, \text{N} \]

5. **Final Answer:**
- The force required to move the cart with constant velocity is approximately:
\[ F \approx 16.67 \, \text{N} \]