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

Question

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 (A) 2 (B)  2√2  (C)  4√2  (D) 8

Tardigrade Admin · Accepted Answer

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 ρ = 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 ( =(F/a) ) exerted will become 4× 2=8 times.

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

2

$22$

$42$

8

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

2

22​

42​

8

$22$

$42$