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Chapter 4 Pressure In Fluids And Atmospheric Pressure | Exercise 4A

Question 48

A force of 50kgf is applied to the smaller piston of a hydraulic machine. Neglecting friction, find the force exerted on the large piston, if the diameters of the pistons are 5cm and 25cm respectively.

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Comparing the diameter of the narrow piston and broader piston = 5/25 or 5:25 = 25:625

Force exerted on narrow piston, F1 = 50kgf

Consider F2 to be the force exerted on the broader piston

We know from the principle of Hydraulic machine,

Pressure on narrow piston = pressure on the broader piston

\begin{array}{l} \frac{\mathrm{F}_{1}}{\mathrm{A}_{1}}=\frac{\mathrm{F}_{2}}{\mathrm{A}_{2}} \\ \frac{\mathrm{F}_{1}}{\mathrm{F}_{2}}=\frac{\mathrm{A}_{1}}{\mathrm{A}_{2}} \\ \Rightarrow 50 / \mathrm{F}_{2}=25 / 625 \\ \mathrm{F}_{2}=1250 \mathrm{kgf} \end{array}

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Question 48

A force of 50kgf is applied to the smaller piston of a hydraulic machine. Neglecting friction, find the force exerted on the large piston, if the diameters of the pistons are 5cm and 25cm respectively.

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

Comparing the diameter of the narrow piston and broader piston = 5/25 or 5:25 = 25:625

Force exerted on narrow piston, F1 = 50kgf

Consider F2 to be the force exerted on the broader piston

We know from the principle of Hydraulic machine,

Pressure on narrow piston = pressure on the broader piston

\begin{array}{l} \frac{\mathrm{F}_{1}}{\mathrm{A}_{1}}=\frac{\mathrm{F}_{2}}{\mathrm{A}_{2}} \\ \frac{\mathrm{F}_{1}}{\mathrm{F}_{2}}=\frac{\mathrm{A}_{1}}{\mathrm{A}_{2}} \\ \Rightarrow 50 / \mathrm{F}_{2}=25 / 625 \\ \mathrm{F}_{2}=1250 \mathrm{kgf} \end{array}

Our top 5% students will be awarded a special scholarship to Lido.

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