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Q. Sand is being dropped on a conveyer belt at the rate of 2 kg per second. The force necessary to keep the belt moving with a constant speed of $3\, ms^{-1}$ will be

AIEEEAIEEE 2012

Solution:

Here, rate of fall of sand on conveyer belt,
$\frac{dm}{dt}=2\,kg\,s^{-1}$
Conveyer belt speed $v = 3\, ms^{-1}$ Force $F = ?$
$F=v \frac{dm}{dt}=3\times2=6N$