The spring of the pressure gauge has a force constant of 1040 N/m, and the piston has a diameter of 1.00 cm. As the gauge is lowered into water, what change in depth causes the piston move in by 0.400 cm

Explanation:

Given data

diameter of piston d= 1cm= 1/100= 0.01m

force F= 1040N/m

distance moved =0.4cm=0.4/100= 0.04m

Area of piston = π^2

= 3.142x (0.01)^2

= 3.142x 0.0001

=0.0003142

=3.142*10-4m^2

Hence to move 0.04m force required

force= pressure * distance

force= 1040* 0.045= 46.8 N

Pressure required = Force / area =  46.8 / 3.142*10-4 = 148949.7 N/ m^2

1000 x 9.81 x h = 148949.7

h =148949.7/9810

h= 15.18m ans