Before going ahead we need to know Pascal’s Law
Pascal’s law state that the change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all point in the fluid.
In a hydraulic jack oil there is enclose hydraulic oil, hence Pascal’s law will apply. Now suppose we have to lift a load off 1000 kg and the bigger piston area is 100 cm2 then Pressure,
p=10 kg/ cm2
If the area of smaller piston is 10 cm2 and according to pascal’s law pressure will be same so, P= 10kg/ cm2
F=P x A
F= 10 x 10
F = 100 kg
Note: Unit of force is N (newton), therefore 1kg force = 1 kg x g (acceleration due to gravity) = 1 x 9.8 = 9.8 N.
In example, we see with the help of 100 kg force we can lift 1000 kg of load. This is called Force Multiplication.
See the both hydraulic jack, if same amount of muscle force if applied on the lever then in which pressure will be more. Remember the pressure formula P=F/A. Because pressure has inversely relation with area, Greater the area lower the pressure. Hence small jack will create more pressure than bigger jack.
We know work= force X displacement.
In the above example let’s consider small piston displaced 10 cm.
Therefore work done= 100 kg.f X 10 cm= 1000 kg.f/cm (kg.f is also a unit of force)