Answer
(a) 93N (b) 94.97 N
Work Step by Step
(a) Let's take,
Force on the input piston = $F_{1}$
Force on the output plunger = $F_{2}$
We know that,
Pressure on the input piston $P_{1}$= Pressure on the output plunger $P_{2}$
So, we can write,
$\frac{F_{1}}{A_{1}}=\frac{F_{2}}{A_{2}}-(1)$
Given that,
$F_{2}=24500\space N$
(1)=>
$F_{1}=F_{2}\times\frac{A_{1}}{A_{2}}=24500\space N[\frac{\pi (7.7\times10^{-3}m)^{2}}{\pi (0.125\space m)^{2}}]=93\space N$
(b) Now,
$P_{1}=P_{2}+h\rho g$
$\frac{F_{1}}{A_{1}}=\frac{F_{2}}{A_{2}}+h\rho g$
$F_{1}=F_{2}\times\frac{A_{1}}{A_{2}}+h\rho g[\pi(7.7\times10^{-3}m)^{2}]$
Let's plug known values into this equation.
$F_{1}=93\space N+1.3\space m\times 830\space kg/m^{3}\times9.8\space m/s^{2}[\pi(7.7\times10^{-3}m)^{2}]=(93+1.97)\space N=94.97\space N$
