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PART - 2 CH - 9 Mechanical Properties of Fluids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 9 Mechanical Properties of Fluids2 Marks
Question
The length of a rectangular tank is 4.0 m and breadth is 3.0 m. It is filled with water up to a height of 2.5 m. Find the total force and water pressure exerted by the water on the bottom of the tank.
✓

Answer

(Density of water $=1000 kg / m ^3$ and $g =10 m / s ^2$ )
Volume of water filled in the tank
$
\begin{array}{l}
=\text { Length } \times \text { breadth } \times \text { height } \\
=4 m \times 3 m \times 2.5 m \\
=30.0 m^3
\end{array}
$
Density of water $=10^3 kg / m ^3$
Mass of water $M =$ Volume $\times$ density
$
\begin{array}{l}
=\left(30.0 m^3\right) \times\left(10^3 kg / m^3\right) \\
=30000 kg=3 \times 10^4 kg
\end{array}
$
Weight of water in the tank
$
\begin{array}{l}
=\text { Mass } \times \text { acceleration due to } \\
\text { gravity }(g) \\
=3 \times 10^4 \times 10=3 \times 10^5 \text { Newton }
\end{array}
$
$\therefore$ Total force on the bottom of the tank
$
\begin{aligned}
F & =\text { Weight of water } \\
& =3 \times 10^5 \text { Newton }
\end{aligned}
$
Area of the bottom
$
\begin{aligned}
A & =\text { Length } \times \text { breadth } \\
& =4 m \times 3 m=12 m^2
\end{aligned}
$
Pressure of water on the bottom
$
\begin{array}{l}
=\frac{\text { Total force on bottom }}{\text { Area of tank }} \\
=\frac{3 \times 10^5}{12}=2.5 \times 10^4 N / m^2 \end{array}
$

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