A sand dropper drops sand of mass m(t) on a conveyor belt at a ra… | JEE Main 2025 Physics PYQ

MCQEasyJEE Main 2025 · 29 January, Shift 2Power

A sand dropper drops sand of mass $m(t)$ on a conveyor belt at a rate proportional to the square root of the speed $v$ of the belt, i.e., $\frac{dm}{dt} \propto \sqrt{v}$ . If $P$ is the power delivered to run the belt at constant speed, then which of the following relationships is true?

A
$P^2 \propto v^3$
B
$P \propto \sqrt{v}$
C
$P \propto v$
D
$P^2 \propto v^5$

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