JEE Main 2025 Jan 29 Shift 2, Physics Q12: Work Energy Theorem And Its Applications

JEE Main2025Jan 29, Shift 2Physics

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

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

Solution

At constant belt speed $v$ , the belt must supply momentum to newly arriving sand. The required thrust is

$F = \frac{d p}{d t} = v \frac{d m}{d t} = v \cdot k v = k v^{3/2}$ .

Power delivered: $P = F v = k v^{5/2}$ , hence $P^{2} \propto v^{5}$ .

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JEE Main 2025 Jan 29 Shift 2, Physics Q12: Work Energy Theorem And Its Applications

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