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  4. Steady rain, giving 5 mm an hour, turns suddenly into a downpour giving 20 mm 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

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Q. Steady rain, giving $5\, mm$ an hour, turns suddenly into a downpour giving $20 \,mm$ 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

Laws of Motion

Solution:

$F=\frac{d p}{d t}=\frac{d}{d t}(m v)$
Here, $v$ is constant, so $F=\frac{v \cdot d m}{d t}$
$\frac{d m}{d t}$ increases by a factor of $\frac{20 mm / hr }{5 mm / hr }=4$ 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