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A hydraulic press has a ram of 15 cm diameter and plunger of 1.5 cm. It is required to lift a weight of 1000 kg. The force required on the plunger is equal to:
1. 10 kg
2. 100 kg
3. 1000 kg
4. 10,000 kg

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Correct Answer - Option 1 : 10 kg

Concept:

Pascal’s Law:

  • It was given by Blaise pascal
  • It is also known as principle of transmission of fluid pressure
  • It states that the pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere.
  • Alternate definition:- The pressure applied to any part of the enclosed liquid will be transmitted equally in all directions through the liquid.

Applications:

  • The underlying principle of hydraulic jack and hydraulic press.
  • Force amplification in the braking system of most motor vehicles.
  • Used in artesian wells, water towers and dams.

Calculation:

Given:

Diameter of plunger, d = 1.5 cm, Diameter of ram, D = 15 cm, weight exerted on the ram, F1 = 1000 kg

According to pascals law,

Pressure applied at plunger = Pressure exerted on the ram

\(\frac{{{F_1}}}{{{A_1}}} = \frac{{{F_2}}}{{{A_2}}}\)

\(\frac{{1000}}{{\frac{{\pi {D^2}}}{4}}} = \frac{{{F_2}}}{{\frac{{\pi {d^2}}}{4}}}\;\)

∴ \({F_2} = \frac{{{d^2}}}{{{D^2}}} \times 1000 = \frac{{{{1.5}^2}}}{{{{15}^2}}} \times 1000 = 10 ~kg\)

Here, F2 = force required on the plunger

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