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{.} $



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