# 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

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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