JEE MAIN - Physics (2022 - 27th July Morning Shift - No. 3)

Sand is being dropped from a stationary dropper at a rate of $$0.5 \,\mathrm{kgs}^{-1}$$ on a conveyor belt moving with a velocity of $$5 \mathrm{~ms}^{-1}$$. The power needed to keep the belt moving with the same velocity will be :
1.25 W
2.5 W
6.25 W
12.5 W

Explanation

$${{dm} \over {dt}} = 0.5$$ kg/s

$$v = 5$$ m/s

$$F = {{vdm} \over {dt}} = 2.5$$ kg m/s2

$$P = \overline F \,.\,\overline v = (2.5)(5)$$ W

$$ = 12.5$$ W

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