Answer
$m=40.77g$
Work Step by Step
Area of petcock is:
$4mm^2*\frac{1m^2}{1000000mm^2}=0.000004m^2$
The force make by the petcock is:
$F=PA=100000Pa*0.000004m^2=0.4N$
And the mass of the petcock is:
$m=\frac{F}{g}=\frac{0.4N}{9.81\frac{m}{s^2}}$
$m=40.77g$
