Laws Of Motion Question 295
Question: Sand is being dropped on a conveyor belt at the rate of$ \text{M kg/s} $ . The force (in N) necessary to keep the belt moving with a constant velocity of $ \text{v m/s} $ will be:
Options:
A) $ r $
B) $ \text{2 Mv} $
C) $ \frac{r}{2} $
D) $ \frac{r}{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ F=\frac{d( Mv )}{dt}=M\frac{dv}{dt}+v\frac{dM}{dt} $
$ \therefore v\text{ is constant,} $
$ \therefore F=v\frac{dM}{dt}\text{ But }\frac{dM}{dt}=Mkg/s $
$ \therefore F=vM\text{ newton}\text{.} $
