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Q.

The height to which a cylindrical vessel be filled with a homogeneous liquid, to make the average force with which the liquid presses the side of the vessel equal to the force exerted by the liquid on the bottom of the vessel, is equal to

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a

Half of the radius of the vessel

b

Three-fourth of the radius of the vessel

c

One-fourth of the radius of the vessel

d

Radius of the vessel

answer is B.

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Detailed Solution

Pressure at the bottom = $h ρ g$
and pressure on the vertical surface = $\frac{1}{2} h ρ g$
Now, according to problem
Force at the bottom = Force on the vertical surface
$\Rightarrow h ρ g \times π r^{2} = \frac{1}{2} h ρ g \times 2 π r h \Rightarrow h = r$

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The height to which a cylindrical vessel be filled with a homogeneous liquid, to make the average force with which the liquid presses the side of the vessel equal to the force exerted by the liquid on the bottom of the vessel, is equal to