Question

The area of cross-section of the wider tube shown in figure is $800{cm}^2$. if 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

Answer: (C)

$15cm$

Given that
$A=800c{m}^3$
$m=12Kg=12000g$
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
$P=h\rho g$
$h=\frac{P}{\rho g}$
$h=\frac{mg}{A\rho g}=\frac{m}{A\rho }$
$h=\frac{12000}{800}$.......($\because \rho =1$)
$\therefore h=15cm$