Question

The height of mercury barometer is 76 cm and density of mercury is 13.6 $\dfrac{g}{{cc}}$ . The corresponding height of water barometer is SI system is:
A) 10.336 m
B) 103.366 m
C) 5.503 m
D) 4.103 m

Answer 1

Hint:In order to find the corresponding height of water barometer we have a formula for it which is ${\rho _1}g{h_1} = {\rho _2}g{h_2}$ (for same pressure) here $\rho ,g,and $h are the density, gravity and height of respective barometers.

Step by step solution:
Step 1:
The solution is straight but before proceeding to it we will read what these barometers are.
Mercury barometer: A mercury barometer is a device that uses the various physical properties of mercury contained in a tube to measure barometric pressure, also known as air pressure or atmospheric pressure. A mercury barometer is a device that uses the physical properties of mercury in a tube to measure barometric pressure.
A Torricellian barometer (sometimes called a mercury barometer) is an inverted (upside-down) glass tube standing in a bath of mercury. Air pressure pushes down on the surface of the mercury, making some rise up the tube. The greater the air pressure, the higher the mercury rises
Water barometer: A barometer in which the changes of atmospheric pressure are indicated by the motion of a column of water instead of mercury. It requires a column of water about thirty-three feet in height.

Step 2:
Now, coming to the question, we are given: The height of mercury barometer is 76 cm =${h_1}$
Density of mercury is 13.6 $\dfrac{g}{{cc}}$=${\rho _1}$ and ${\rho _2}$ =1
For same pressure ${\rho _1}g{h_1} = {\rho _2}g{h_2}$
Substituting the values and g get cancel, we get ${h_2}$ =$\dfrac{{76 \times 13.6}}{1}$ which is equal to 1033.6cm
Converting it to SI system we get 10.336 m
Hence, the corresponding height of water barometer is SI system is: 10.336 m

Option A is correct.

Additional information:
-Measurement of atmospheric pressure
-Determining the altitude of a place
-Whether forecasting
-Calibration and checking of aneroid barometers
-Application in fluid mechanics
-Measurement of pressure in aircrafts
-Surface weather analysis
-Preparation of barographs
-Usage in physical sciences like physics, astronomy and chemistry
-Preparation of aircraft altimeters.

Note:The values must be substituted correctly and do not forget to mention the correct SI system when answering. Give separate names to the respective density and height so that there is no confusion in the values.