A large open tank containing water has two holes to its wall. A square hole of side 'a' is made at a depth 'y' and a circular hole of radius 'r' is made at a depth '

Question

A large open tank containing water has two holes to its wall. A square hole of side 'a' is made at a depth 'y' and a circular hole of radius 'r' is made at a depth '16y'from the surface of water. If equal amount of water comes out through both the holes per second, then the relation between 'r' and 'a' will be

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Answer:

B

Solution:

(A) $v_{1} A_{1} = v_{2} A_{2}$ $2 g h_{1} A_{1} = 2 g h_{2} A_{2}$ $y a^{2} = 16 y π r^{2}$ $a^{2} = 4 π r^{2}$ $r = \frac{a}{2 π}$

TestHub · Accepted Answer

(A) v 1 ​ A 1 ​ = v 2 ​ A 2 ​ 2 g h 1 ​ ​ A 1 ​ = 2 g h 2 ​ ​ A 2 ​ y ​ a 2 = 16 ​ y π r 2 a 2 = 4 π r 2 r = 2 π ​ a ​

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