Question

More weight was required at to attain equilibrium. Is it not due to the increased surface area of water at that end?

Answer 1

Yes

It is the figure of a hydraulic jack. Two cylinders of different area of cross-section, filled with water, are connected using a pipe. 

A₁ is the area of cross-section of the smaller piston and A₂, that of the bigger one. When a force F₁ is applied on the piston X, a force F₂ will be experienced on the piston Y. Then according to Pascal’s Law, pressure applied on the side X will be equal to the pressure experienced on the side Y. 

So P_x = P_y

Since P = \(\frac{F}{A}\)

\(\frac{F_1}{A_1}=\frac{F_2}{A_2}\)

If the area of cross-section of the 100 times that of the first piston

A₂ = 100A, 

Therefore A₂ /A₁ = 100 

F₂ = 100F₁ 

That means the large piston will experience a force of 100N when a force of 1N is applied on the small piston. The amount of work done on the two dies of the tube is equal. Therefore if the section Y is to be raised by 1cm, the section X has to be lowered by 100cm.