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JIPMER 2015
Exam
JIPMER
Year
2015
Subject
Physics
Chapter
Mechanical Properties of Fluids

JIPMER 2015 · Physics · Mechanical Properties of Fluids

Water level is maintained in a cylindrical vessel upto a fixed...

Water level is maintained in a cylindrical vessel upto a fixed height HH. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel, so that the water stream coming out of the hole strikes the horizontal plane of the greatest distance from the vessel? Water level is maintained in a cylindrical vessel upto a fixed height H . The vessel is kept on a horizontal plane. At

Options

  1. Ah=H2h=\frac{H}{2}
  2. Bh=3H2h=\frac{3 H}{2}
  3. Ch=2H3h=\frac{2 H}{3}
  4. Dh=34Hh=\frac{3}{4} H

Correct answer

A. h=H2h=\frac{H}{2}

Step-by-step solution

The velocity with which water will came out v=2g(H−h)v=\sqrt{2 g(H-h)} The time of flight of water ejected from the hole. t=2hg= time of flight ∴x=v×t=2g(H−h)×2hg=4(Hh−h2)\begin{aligned} t & =\sqrt{\frac{2 h}{g}}=\text{ time of flight } \\ \therefore \quad x & =v \times t \\ & =\sqrt{2 g(H-h)} \times \sqrt{\frac{2 h}{g}}=\sqrt{4\left(H h-h^2\right)}\end{aligned} For xx to be maximum dxdh=0⇒d4(Hh−h2)dh=0⇒0=H−2h⇒h=H2\begin{aligned} & \frac{d x}{d h}=0 \\ \Rightarrow & d \frac{\sqrt{4\left(H h-h^2\right)}}{d h}=0 \\ \Rightarrow & 0=H-2 h \Rightarrow h=\frac{H}{2}\end{aligned}
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