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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.
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.
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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