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  • A cylindrical jar has radius r. To what height h should it be filled with a liquid so that the force exerted by the liquid on the sides of the jar equals the force exerted on the bottom?<d

A cylindrical jar has radius r. To what height h should it be filled with a liquid so that the force exerted by the liquid on the sides of the jar equals the force exerted on the bottom?

Option: 1

\mathrm{h=\frac{r}{2}}


Option: 2

\mathrm{h=r}


Option: 3

\mathrm{h=2 r}


Option: 4

\mathrm{h=4 r}


Answers (1)

best_answer

Let a cylinder with radius r be filled with a homogeneous liquid of density \mathrm{\rho} up to a height h. Pressure at the bottom of the cylinder, \mathrm{p_1=\rho g h} Pressure at the top of the liquid surface, \mathrm{p_2=0} Average pressure on the sides of the cylinder,

\mathrm{ p=\frac{p_1+p_2}{2}=\rho g h / 2 }
Force on the sides of the vessel = average pressure \times
\mathrm{ \begin{gathered} \text { area }=\frac{\rho g h}{2} \times 2 \pi r h \\ =\pi r \rho g h^2 \end{gathered} }
Force on the bottom of the vessel \mathrm{=p_1 \pi r^2 =\rho g h \pi r^2}
Two forces will be equal if

\mathrm{ \pi r \rho g h^2=\rho g h \pi r^2 }
or \mathrm{ h=r }

Posted by

Ritika Kankaria

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