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

Diameter of smaller piston `=1.0cm`
`therefore` Radius `r_(1)=0.5cm=0.5xx10^(-2)m`
Diameter of large pistion `=3.0cm`
`therefore` Radius `r_(2)=1.5cm=1.5xx10^(-2)m`
Force exerted on the smaller piston `F_(1)=10N`
Force exerted on the larger piston `F_(2)=?`
Displacement of smaller piston ,
`L_(1)=6.0cm=6xx10^(-2)m`
Displacement of larger piston , `L_(2)=?`
(a) From Pascal.s law ,
`(F_(1))/(A_(1))=(F_(2))/(A_(2))`
`thereforeF_(2)=F_(1)xx(A_(2))/(A_(1))`
`=10xx(pixx(1.5xx10^(-2))^(2))/(pixx(0.5xx10^(-2))^(2))`
`=10xx(3)^(2)`
`=90N`
(b) If the smaller piston is pushed in throgh `L_(1)` and the larger piston move out `L_(2)` , then volume covered by the movement of smaller piston inwards is equal to volume moved outwards due to the larger piston.
`L_(1)A_(1)=L_(2)A_(2)[because"Volume"="length"xx"area"]`
`thereforeL_(2)=L_(1)xx(A_(1))/(A_(2))`
`=6xx10^(-2)xx(pixx(0.5xx10^(-2))^(2))/(pixx(1.5xx10^(-2))^(2))`
`=6xx10^(-2)xx((1)/(3))^(2)`
`thereforeL_(2)=(6xx10^(-2))/(9)`
`=0.67xx10^(-2)m`
`=0.67cm`
Atmospheric pressure is common to both piston and has been ignored.