# A hydraulic press has a ram of 20 cm diameter and a plunger of 3 cm diameter. It is used for lifting a weight of 30 kN. Find the force required at the

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A hydraulic press has a ram of 20 cm diameter and a plunger of 3 cm diameter. It is used for lifting a weight of 30 kN. Find the force required at the plunger.

1. 975 N
2. 1075 N
3. 875 N
4. 675 N

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Correct Answer - Option 4 : 675 N

Concept:

Pascal’s Law:

• It was given by Blaise pascal
• It is also known as the 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 = 3 cm, Diameter of ram, D = 20 cm, Force required at the plunger = ?, Weight = 30 kN

According to pascals law,

Pressure applied at ram = Pressure exerted on the plunger

$\frac{{{F_1}}}{{{A_1}}} = \frac{{{F_2}}}{{{A_2}}}$

$\frac{{30000}}{{\frac{{\pi {D^2}}}{4}}} = \frac{{{F_2}}}{{\frac{{\pi {d^2}}}{4}}}\;$

∴ ${F_2} = \frac{{{d^2}}}{{{D^2}}} \times 30000 = \frac{{{{3}^2}}}{{{{20}^2}}} \times 30000 = 675\; kN$

Here, F2 = force required on the plunger