Question

Steady rain, giving $5mm$ an hour, turns suddenly into a downpour giving $20mm$ an hour and the speed of the rain drops falling vertically on to a flat roof simultaneously doubles. The pressure exerted by the falling rain on the roof is raised by a factor of

• A. 4
• B. 8
• C. 16
• D. 32

Answer 1

Answer: (B)

$F=\frac{dp}{dt}=\frac{d}{dt}(mv)$
Here, $v$ is constant, so $F=\frac{v\cdot dm}{dt}$
$\frac{dm}{dt}$ increases by a factor of $\frac{20mm/hr}{5mm/hr}=4$ and $v$ increases
by a factor of $2.$ Hence $F$ increases by a factor of 8 .
$P=\frac{F}{A},$ hence pressure increases by a factor of 8