# A hydraulic press has a ram of 300 mm diameter and a plunger of 45 mm diameter. When the force applied at the plunger is 50 N, the weight lifted by th

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A hydraulic press has a ram of 300 mm diameter and a plunger of 45 mm diameter. When the force applied at the plunger is 50 N, the weight lifted by the hydraulic press will be nearly
1. 2133 N
2. 2223 N
3. 2316 N
4. 2406 N

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Correct Answer - Option 2 : 2223 N

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 = 45 mm

Diameter of ram, D = 300 mm

Force applied at plunger, F1 = 50N

According to pascals law,

Pressure applied at plunger = Pressure exerted on the ram

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

$\frac{{50}}{{\frac{{\pi {d^2}}}{4}}} = \frac{{{F_2}}}{{\frac{{\pi {D^2}}}{4}}}\;$

${F_2} = \frac{{{D^2}}}{{{d^2}}} \times 50 = \frac{{{{300}^2}}}{{{{45}^2}}} \times 50 = \;2222.22N$

Here, F2 = force exerted by the ram to lift the weight.