Question

Steady rain, giving 5 mm an hour, turns suddenly into a downpour 2 mm an hour and the speed of rain drops falling vertically on to a flat roof simultaneously doubles. The pressure exerted by the falling rain on the roof rises by a factor of

Answer 1

The pressure exerted by the falling rain on the roof rises by a factor of 8.

Explanation:

F = ma

In this case we can write.

dF = (dm)a = (dm) x dv/dt = (dv)(dm/dt)

As rain increased by the the factor of 4 from 5 mm to 20 mm and the volume and density of the rain drop is constant.

Mass of rain drops falling down also increased by the factor of 4.

dm/dt = 4

Velocity of rain drop is increased by factor of 2.

so, dv = 2

dF = (dv)(dm/dt) = 2 x 4 =8

As area is constant.

dp ~ d f = 8

Thus the pressure exerted by the falling rain on the roof rises by a factor of 8.

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