Question

The area of cross-section of the wider tube show in figure is $800c{m}^2$. If a mass of $12kg$ is placed on the massless piston, the difference in heights $h$ in the level of water in the two tubes is :

• A. $10cm$
• B. $6cm$
• C. $15cm$
• D. $2cm$

Answer 1

The correct option is C $15cm$

Given that:
$A=800c{m}^2$
$m=12kg=12000g$
Here, the force on piston is $F=mg$
Hence, increase in pressure on the liquid in the wider tube is
$P=\frac{F}{A}=\frac{mg}{A}$
Since, h is the difference in level of water in the two tubes, thus
$P=h\rho g$
$h=\frac{P}{\rho g}$
$h=\frac{mg}{A\rho g}=\frac{m}{A\rho }$
$h=\frac{12000}{800}$.......($\because \rho =1$)
$\therefore h=15cm$