Question

On a conveyor belt moving with a speed u, sand falls at a constant rate $\frac{dm}{dt}$ where m is the mass of sand. The extra force required to maintain the speed of

• A. $m\frac{du}{dt}$
• B. mu
• C. $\frac{dm}{dt}/u$
• D. $u\frac{dm}{dt}$
• E. $\frac1{m} \frac{du}{dt}$

Answer 1

The Correct Option is B

We are given a conveyor belt moving with a speed \( u \), and sand is falling at a constant rate \( \frac{dm}{dt} \), where \( m \) is the mass of sand. We need to determine the extra force required to maintain the speed of the conveyor belt.

To solve this, let's use the concept of momentum and the principle of conservation of momentum. The rate of change of momentum is given by: \[ F_{\text{extra}} = \frac{d}{dt} (m \cdot u) \] Since the mass is falling at a constant rate, \( m \) increases with time. Therefore, the total momentum of the system is: \[ m \cdot u \] The extra force required to maintain the speed \( u \) of the conveyor belt is the rate of change of momentum, which is: \[ F_{\text{extra}} = \frac{d}{dt}(m \cdot u) = \frac{dm}{dt} \cdot u \] This shows that the extra force required is: \[ F_{\text{extra}} = m \cdot u \]

Correct Answer:

Correct Answer: (B) mu