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Concepts Of Physics MCQ Edition [Volume 1]PhysicsFluid Mechanics

As depicted in the figure, the heights of the mercury surfaces in the two arms of a manometer are 2 cm and 8 cm . The atmospheric pressure is given as 1.01 10^5 N m ⁻² . Calculate the pressure of the gas enclosed in the cylinder.

Options

  1. A0.93 10^5 N m ⁻²
  2. B1.01 10^5 N m ⁻²
  3. C1.09 10^5 N m ⁻²
  4. D1.12 10^5 N m ⁻²

Correct answer

C. 1.09 10^5 N m ⁻²

Step-by-step solution

From the given figure, the mercury level in the open arm is higher than that in the arm connected to the gas cylinder. This indicates that the gas pressure is greater than the atmospheric pressure. The difference in the height of the mercury levels is: h = 8 cm - 2 cm = 6 cm = 0.06 m The gauge pressure of the gas is given by: P = g h Substituting the standard values for the density of mercury ( = 13.6 10^3 kg m ⁻³ ) and acceleration due to gravity ( g = 9.8 m s ⁻² ): P = 13.6 10^3 9.8 0.06 P = 7996.8 N m ⁻² 0.08 10

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