Question

A cylindrical diving bell, whose length is 150 cm is lowered to the bottom of the tank. The rock is found to rise 50 cm into the bell. Assuming the atmospheric pressure at the sunrise equivalent to 1000 cm of the water and the temperature as constant the depth of the tank

Answer 1

Hint:- Pressure is defined as the ratio of force applied and the area of cross section. We can express the value of pressure in terms of height. The pressure acting on a same point in the liquid surface will be equal to each other. The gauge pressure is the summation of atmospheric pressure and absolute pressure.

Formula used: The formula of pressure at a point is given by,
$P = {P_{liquid}} \cdot h$
Where P is the pressure ${P_{liquid}}$ is the pressure of the liquid and h is the height of the liquid from the surface of the liquid.

Complete step-by-step solution:It is given in the problem that a cylindrical bell of length 150 cm is lowered to the bottom of the tank. The bell is found to raise 50 cm from the bottom the equivalent atmospheric pressure is 1000 cm of water and the temperature remains constant and we need to find the value of total depth of the tank.
The pressure inside the tank is given as,
$ \Rightarrow P = {P_o} + {P_{liquid}} \cdot h$
Replace the value of atmospheric pressure height of the cylindrical bell from the surface of liquid and pressure of the liquid.
$ \Rightarrow P = {P_o} + \left( {h - 50} \right)$………eq. (1)
Also the pressure inside the tank is given by,
$ \Rightarrow P = {P_{liquid}} \cdot h$
Replace the value of ${P_{liquid}} = 1000cm$ and $h = 150cm$ we get,
\[P = 1000 \times 150\]………eq. (2)
Equating equation (1) and equation (2) we get,
$ \Rightarrow {P_o} + \left( {h - 50} \right) = 1000 \times 150$
$ \Rightarrow 1000 + \left( {h - 50} \right) = 1000 \times 150$
$ \Rightarrow 950 + h = 1000 \times 150$
$ \Rightarrow h = 550cm$.
The height of the tank is equal to$h = 550cm$.

Note:- The pressure on the surface is given in height so we have solved it in height only and it is advisable to students to convert all the units into similar ones and also remember the formula of pressure in terms of height.