Question

Gravels are dropped on a conveyer belt at the rate of $0.5{kgs}^{-1}$. The extra force required in newtons to keep the belt moving at $2{ms}^{-1}$ is:

• A. $0.5$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is B $1$

Force is the rate of momentum. so, $F=\frac{d\left(mv\right)}{dt}=m\frac{dv}{dt}+v\frac{dm}{dt}$

here, $v$ is constant , so $\frac{dv}{dt}=0$ and given $\frac{dm}{dt}=0.5kg{s}^{-1}$

Thus the extra force required $=F=2\times 0.5=1N$