Question

The Heights of mercury surface in the two arms of the manometer shown are 2 cm and 8 cm. find the pressure of the gas in the cylinder? P_atm = 10⁵ N/m²

The density of mercury $=13600\frac{kg}{m^3}$. Acceleration due to gravity $g=10\frac{m}{s^2}$

• A. 1.08 × 10⁵ N/m²
• B. 1.08 × 10⁵ N/cm²
• C. 1.08 × 10⁶ N/m²
• D. 1.08 × 10⁶ N/cm²

Answer 1

The correct option is B

1.08 × 10⁵ N/cm²

Pressure of gas contained in the chamber$P_g$ = Atmospheric pressure$P_0$ + pressure due to the (8-2=6cm) mercury column.

$P_g=P_0+\rho gh$

Where h = (8 - 2)cm = 6 cm =0.06 m

The density of mercury $\rho =13600\frac{kg}{m^3}$.

Atmospheric pressure$P_0={10}^{5}Pa$

$P_g={10}^5+(13600\times 10\times \frac{6}{100})$

$=108160\frac{N}{m^2}$
$=1.08160\times {10}^{5}Pa$