Question

For the system shown in the figure, the cylinder on the left at $L$ has a mass of $600kg$ and a cross-sectional area of $800c{m}^2$. The piston on the right, at $S$, has cross-sectional area $25c{m}^2$ and negligible weight. If the apparatus is filled with oil $\left(\rho =0.75g/c{m}^3\right)$. The force $F$ (in $N$) required to hold the system in equilibrium is____. Take $g=10m/s^2$

Answer 1

Answer: 37.50

In equilibrium $\frac{600\times 10}{800\times 10^{-4}}$
$=\frac{F}{25\times 10^{-4}}+h\rho g$
$\Rightarrow \frac{F}{25\times 10^{-4}}=\frac{60}{8}\times 10^4-8\times \left(0.75\times 10^3\right)\times 10$
$\frac{F}{25\times 10^{-4}}=1.5\times 10^4$
$\Rightarrow F=37.5N$