Question

Sand is being dropped on a conveyer belt at the rate of $Mkg/s$. The force necessary to keep the belt moving with a constant velocity of $vm/s$ will be

• A. $\frac{Mv}{2}N$
• B. Zero
• C. $MvN$
• D. $2MvN$

Answer 1

The correct option is C $MvN$

According to Newton’s second law, force is equal to rate of change of momentum.

$F=\frac{dp}{dt}=\frac{d}{dt}\left(mv\right)$

$\Rightarrow F=m\frac{dv}{dt}+v\frac{dm}{dt}$
(using product rule)

$\Rightarrow F=v\frac{dm}{dt}=MvN$ is the force required.

(because velocity is constant)