MHT CET · Physics · Mechanical Properties of Fluids
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
- A \(r=\frac{2 a}{\pi}\)
- B \(r=\frac{a}{2 \sqrt{\pi}}\)
- C \(r=\frac{a}{2 \pi}\)
- D \(r=\frac{2 a}{\sqrt{\pi}}\)
Answer & Solution
Correct Answer
(B) \(r=\frac{a}{2 \sqrt{\pi}}\)
Step-by-step Solution
Detailed explanation
(A)
\(v_{1} A_{1}=v_{2} A_{2}\)
\(\sqrt{2 g h_{1}} A_{1}=\sqrt{2 g h_{2}} A_{2}\)
\(\sqrt{y} a^{2}=\sqrt{16} y \pi r^{2}\)
\(a^{2}=4 \pi r^{2}\)
\(r=\frac{a}{2 \sqrt{\pi}}\)
\(v_{1} A_{1}=v_{2} A_{2}\)
\(\sqrt{2 g h_{1}} A_{1}=\sqrt{2 g h_{2}} A_{2}\)
\(\sqrt{y} a^{2}=\sqrt{16} y \pi r^{2}\)
\(a^{2}=4 \pi r^{2}\)
\(r=\frac{a}{2 \sqrt{\pi}}\)
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