Question

Q.9 The height of mercury column
in a barometer in a Calcutta laboratory
was recorded to be 75 cm. Calculate
this pressure in SI system and C.G.S.
unit (given specific gravity of mercury
=13.6, density of water=10° Kg/mº​

Answer 1

Answer:

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) = 9.8m/s  

2

 

Density of the Water =10  

3

kg/m  

3

.

=1000kg/m  

3

 

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

    = 1300kg/m  

3

.

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) = 9.8m/s  

2

 

=9.8×100cm/s  

2

 

=980cm/s  

2

.

Density of the Water =1000kg/m  

3

.

= 1000×10  

6

g/10  

6

cm  

3

.

= 10  

6

/10  

6

g/cm  

3

.

= 1g/cm  

3

 

∴ Density of the Mercury(ρ) = Specific Gravity of the Mercury × Density of the Water.

=1.3×1

=1.3g/cm  

3

.

Now Using the Formula,

 Pressure(P)= hρg

   = 75×1.3×980

   = 9550 Ba.

Hence the Pressure is 9550 barye.

Explanation: