10. 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 = 10 kg/mº, g = 9.8 m/s’ at Calcutta. Pressure
= hpg in usual symbols.
Answers
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.