The height of mercury coloumn in a barometer in Calcutta lab was recoreded to be 75 cm. Calculate this pressure in SI and CGS units using following data: Specific Gravity of mercury = 13.6, Density of water = 1000 kg/metre(cubed), g = 9.8 m/second (squared) at Calcutta. Given P = hpg in usual symbols.

Question

AskIITians Expert Hari Shankar IITD · Answer

Pressure = hpg = (75 cm)(13.6 * 1000 kg/m³)(9.8 m/s²)

SI units

We only need to convert cm to m, since all other units are already SI.

So, pressure in SI units = (0.75 m)(13.6 * 1000 kg/m³)(9.8 m/s²) = 99960 bar

CGS units

Here, we need to convert kg/m3 to g/cm³ and m/s² to cm/s²

1 kg/m³ = 1000 g/m³ * (1 m/100 cm)³ = 1000 g / 1000000 cm³ = 0.001g/cm³ .

So 1000 kg/m³ = 0.001 * 1000 g/cm³

= 1 g/cm³

1 m/s² = 100 cm/s²

So, 9.8 m/s² = 980 cm/s² .

Therefore, Pressure in CGS units = (75 cm)(13.6 * 1 g/cm³)(980 cm/s²) = 999600 g/cm-s²

For easy conversion between units, remember that multiplying by 1 does not make any difference. So to convert 1 m to 100 cm, you can multiply 1 m by (100cm/1 m), since (100cm/1m) is 1. This is useful when you have big units. eg. to convert kg-m/torr to g-mm/Pa, just multiply with (1000g/1kg)*(1000mm/1m)*(760 torr/10125 Pa) etc.

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