Two large, identical water tanks, 1 and 2, kept on the top of a building of height H, are filled with water up to height h in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected

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Two large, identical water tanks, 1 and 2, kept on the top of a building of height H, are filled with water up to height h in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2 , and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are t_1 and t_2, respectively. If H= ( 16 9 ) h, then the ratio t_1 / t_2 is _______ .

Quantrex Academy · Accepted Answer

Correct answer: A. A

aligned & Av = av _1 \ & ~A (- dy dt )= a 2 gy ; dt = A a 2 ~g -d y y \ & _0^ t_1 dt = A a 2 ~g _ h ^0- d y y \ & t_1= A a 2 ~g 2 h ; t _1= A a 2 h g aligned A v^ = av _2 aligned & A (- d y d t )=a 2 g(H+y) \ & d t=- A a 2 g d y H+y \ & _0^ t_2 d t=- A a 2 g _H^0 d y H+y \ & t_2= A a 2 g (2)( H+h - H ) \& H= 16 h 9 \ & = A a 2 h g ( 5 3 - 4 3 ) \ & t_2= A a 2 h g ( 1 3 ) aligned ratio t _1 t _2 =3

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