First slide

Pressure in a fluid-mechanical properties of fluids

Question

For the system shown in the figure, the cylinder on the left at L has a mass of 600 kg and a cross-sectional area of 800 cm².The piston on the right, at S, has cross-sectional area 25 cm² and negligible weight. If the apparatus is filled with oil $(ρ = 0.75 g / {cm}^{3})$ . The force F (in N) required to hold the system in equilibrium is _______.
Take g= 10 m/s².

Moderate

Solution

$In equilibrium \frac{600 \times 10}{800 \times 10^{- 4}} = \frac{F}{25 \times 10^{- 4}} + h ρ g$
$\begin{array}{l} \Rightarrow \frac{F}{25 \times 10^{- 4}} = \frac{60}{8} \times 10^{4} - 8 \times (0.75 \times 10^{3}) \times 10 \\ \frac{F}{25 \times 10^{- 4}} = 1.5 \times 10^{4} \\ \Rightarrow F = 37.5 N \end{array}$

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