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