Question

What is the pressure on the swimmer who is 10m below the surface of the lake?

Answer 1

Hint: Pressure on the swimmer will be due to the atmospheric pressure and the column of water of height 10m above him. Pressure is given by the product of height which in this case in depth, density and acceleration due to gravity. Substitute the values in the formula \[P = h\rho g\] and simplify to get the pressure on the swimmer.

Complete step-by-step solution
When an object is below any fluid, it experiences some pressure from the top. This pressure is due to the column of fluid above that body and it is given by:
 \[P = h\rho g\]
Where P is the pressure exerted on the body
H is the height of the fluid column
 \[\rho \] is the density of the fluid
g is the acceleration due to gravity.
When a swimmer is swimming 10m below the surface of water, he experiences pressure due to the water column above him in addition to the atmospheric pressure. The atmospheric pressure is caused due to the envelope of air above the earth and its value is 1 atm or \[1.01 \times {10^5}\] Pa. So the total pressure on the swimmer will be
 \[
  P = 1.01 \times {10^5} + h\rho g \\
  P = 1.01 \times {10^5} + 10 \times 1000 \times 9.81 = 1.01 \times {10^5} + 0.98 \times {10^5} \\
  P = 1.99 \times {10^5} \\
 \]
Therefore, the correct answer is \[1.99 \times {10^5}\] pascal

Note
The value of atmospheric pressure can be appreciated by imagining it using the following analogy.
We know that the atmospheric pressure \[P = 1.01 \times {10^5}Pa\] . Let’s say that a human standing on ground takes the area \[A = 1{m^2}\] . So to equate the pressure on this area, the weight required is w=101000N (assuming g=10 \[m/{s^2}\] ). So effectively this is equivalent to 100 motorcycles. Which means, on a daily basis we carry  ~100 motorcycles on our heads.