Question:
A truck carrying sand having a total mass of 1600 kg is moving with a uniform velocity of 15 m s$^{-1}$. Sand is dropped into it at a rate of 24 kg min$^{-1}$. The force needed to keep the truck moving with uniform velocity is:
A truck carrying sand having a total mass of 1600 kg is moving with a uniform velocity of 15 m s$^{-1}$. Sand is dropped into it at a rate of 24 kg min$^{-1}$. The force needed to keep the truck moving with uniform velocity is:
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In variable mass systems, always consider momentum flux: \(F = \frac{dm}{dt} \cdot v\).
Updated On: Jul 18, 2026
- 6 N
- 1.6 N
- 40 N
- 4 N
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The Correct Option is A
Solution and Explanation
Step 1: Understanding variable mass system.
This is a variable mass problem where sand is added to a moving truck. External force is required to maintain constant velocity due to momentum change.
Step 2: Convert mass flow rate into SI units.
\[ 24 \, \text{kg min}^{-1} = \frac{24}{60} = 0.4 \, \text{kg s}^{-1} \]
Step 3: Concept of force in variable mass system.
Force required is given by: \[ F = \frac{dm}{dt} \cdot v \] since incoming sand has zero horizontal velocity initially.
Step 4: Substitute values.
\[ F = 0.4 \times 15 \] \[ F = 6 \, \text{N} \]
Step 5: Physical interpretation.
The force is required to accelerate incoming sand from 0 to 15 m/s, hence external force is needed.
Step 6: Final conclusion.
Therefore, \[ \boxed{6 \, \text{N}} \]
This is a variable mass problem where sand is added to a moving truck. External force is required to maintain constant velocity due to momentum change.
Step 2: Convert mass flow rate into SI units.
\[ 24 \, \text{kg min}^{-1} = \frac{24}{60} = 0.4 \, \text{kg s}^{-1} \]
Step 3: Concept of force in variable mass system.
Force required is given by: \[ F = \frac{dm}{dt} \cdot v \] since incoming sand has zero horizontal velocity initially.
Step 4: Substitute values.
\[ F = 0.4 \times 15 \] \[ F = 6 \, \text{N} \]
Step 5: Physical interpretation.
The force is required to accelerate incoming sand from 0 to 15 m/s, hence external force is needed.
Step 6: Final conclusion.
Therefore, \[ \boxed{6 \, \text{N}} \]
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