Laws of Motion - Result Question 6
6. Sand is being dropped on a conveyor belt at the rate of $M kg / s$. The force necessary to keep the belt moving with a constant velocity of $v m / s$ will be:
[2008]
(a) Mv newton
(b) 2 Mv newton
(c) $\frac{Mv}{2}$ newton
(d) zero
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Answer:
Correct Answer: 6. (a)
Solution:
(a) $F=\frac{d(Mv)}{dt}=M \frac{dv}{dt}+v \frac{dM}{dt}$
$\therefore v$ is constant,
$\therefore F=v \frac{dM}{dt}$ But $\frac{dM}{dt}=Mkg / s$
$\therefore F=vM$ newton.
