WBJEE · Physics · Mechanical Properties of Fluids
Water in filled in a cylindrical vessel of height H. A hole is made at height z from the bottom, as shown in the figure.
The value of of z for which the range (R) of the emerging water through the hole will be maximum for
- A \(z=\frac{H}{4}\)
- B \(\quad z=\frac{\mathrm{H}}{2}\)
- C \(z=\frac{\mathrm{H}}{8}\)
- D \(\quad z=\frac{H}{3}\)
Answer & Solution
Correct Answer
(B) \(\quad z=\frac{\mathrm{H}}{2}\)
Step-by-step Solution
Detailed explanation
\(x=2 \sqrt{y(H-y)}\) If hole is made at depth \(y=H-y\), then \(\begin{aligned} & X=2 \sqrt{(H-y)[H-(H-y)]} \\ & =2 \sqrt{y(H-y)} \\ & =x \end{aligned}\) Hence, range will remain same. Now, \(\frac{d X}{d y}=\frac{1}{2}\left(y H-y^2\right)^{-1 / 2}(H-2 y)\) For maximum value of…
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