Question

The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = 13.6, Density of water = 103 kg/m3, g = 9.8 in/s2 at Calcutta. Pressure = hρg in usual symbols.

Concept of Physics - 1 , HC VERMA , Chapter "Introduction to Physics".

Answer 1

Hello Dear.

Given ⇒ 

Height of the Mercury Column in a Barometer = 75 cm.

For Finding the Pressure in S.I. System, Changing 75 cm into meter.

∴ Height of the Mercury column(h) = 75 cm.
    = 0.75 m.

Acceleration due to gravity(g) = 9.8 m/s².
Density of the Water = 10³ kg/m³.
= 1000 kg/m³
Specific Gravity of the Mercury = 13.6

Specific Gravity of the Substance is the Ratio of the Density of the Substance to the Density of the Water.

∴ Specific Gravity = Density of the Substance /Density of the Water.
⇒ Density of the Mercury(ρ) = 1.3 × 1000
     = 1300 kg/m³.


Now,
Using the Formula,
  Pressure(P) = hρg
   = 0.75 × 1300 × 9.8
   = 9555 Pa.

Hence, the Pressure is 9555 Pa.


For Finding the Pressure in C.G.S. System,

Height of the Mercury Column(h) = 75 cm.
Acceleration due to gravity(g) = 9.8 m/s²
= 9.8 × 100 cm/s².
= 980 cm/s².

Density of the Water = 1000 kg/m³.
 = 1000 × 10³g/10⁶ cm³.
 = 10⁶/10⁶ g/cm³.
 = 1 g/cm³

∴ Density of the Mercury(ρ) = Specific Gravity of the Mercury × Density of the Water.
= 1.3 × 1
= 1.3 g/cm³.


Now Using the Formula,

  Pressure(P)= hρg
    = 75 × 1.3 × 980
    = 9550 Ba.


Hence the Pressure is 9550 barye.



Hope it helps.

Answer 2

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