Two syringes of different cross sections (without needles)filled with water are connected with a tightly fitted rubber tube filled with water .Diameters of the smaller piston and larger piston 1.0 cm and 3.0 cm respectively .(a)Find the force exerted on the large piston when a force of 10 N is applied to the smaller piston .(b) If the smaller piston is pushed in through 6.0 cm how much does the larger piston move out ?

Explanation

(a) Since pressure is transmitted underdiminished throughout the fluid,
`F_2=A_2/A_1F_1= (pi(3//2 times 10^-2 m)^2)/(pi(1//2 times 10^-2 m)^2) times 10N`
=90 N
(b) Water is considered to be perfectly incompressible. Volume covered by the movement of smaller piston inwards is equal to volume moved outwards due to the larger piston.
`L_1A_1=L_2A_2`
`L_2=A_1/A_2 L_1=(pi(1//2 times 10^-2 m)^2)/(pi(3//2 times 10^-2 m)^2) times 6 times 10^-2 m`
`=0.67 times 10^-2 m=0.67 cm`
Note, atmospheric pressure is common to both pistons and has been ignored.