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

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

JamiaJamia 2010

Solution:

Force exerted by the falling rain drop on the roof $ =adpv $ where, $ a= $ area of the roof $ d= $ thickness of water layer formed due to rain $ \rho = $ density of water and $ v= $ velocity of rain drops Since, rain falling suddenly increases from 5 mm/h to 20 mm/h, hence d increases to 4 times velocity is also doubled. Hence, becomes $ 2v $ . Thus, the pressure $ \left( =\frac{F}{a} \right) $ exerted will become $ 4\times 2=8 $ times.