Question

A tank of size \[10m\times 10m\times 10m\] is full of water and built on the ground. If g = 10 \[m{{s}^{-2}}\], the potential energy of the water in the tank is:
A. \[5\times {{10}^{7}}\] J
B. \[1\times {{10}^{8}}\] J
C. \[5\times {{10}^{4}}\] J
D. \[5\times {{10}^{5}}\] J

Answer 1

Hint: In this question, we are asked to calculate the potential energy of water in a tank. To solve this question, we will be assuming the mass of evenly distributed water in a tank to be concentrated at the centre of gravity. We also know that potential energy is given as the product of mass, acceleration due to gravity and the height of the object from ground.

Formula Used:
- \[P.E=mgh\]
\[\rho =\dfrac{m}{v}\]

Complete step by step answer:
 It is given that the tank has dimensions of \[10m\times 10m\times 10m\]. Therefore, the volume of the tank is V = \[{{10}^{3}}{{m}^{3}}\]. Assuming the tank is completely filled with water the volume of water and tank will be the same. We also know that density is 1000 \[kg/{{m}^{3}}\].
We know,
\[\rho =\dfrac{m}{v}\]
Therefore, mass of water is given as
\[m=\rho v\]
After substituting values
We get,
\[m={{10}^{3}}\times {{10}^{3}}\]
Therefore,
\[m={{10}^{6}}\] kg
Now, this mass of water can be assumed to be concentrated at the centre of gravity of the system.
Therefore, this mass will be at a height of 5 m from the ground
We know,
\[P.E=mgh\]
After substituting the values
We get,
\[P.E={{10}^{6}}\times 10\times 5\]
Therefore,
\[P.E=5\times {{10}^{7}}\] J
Therefore, the correct answer is option A.

Note: The potential energy is the energy that is stored in an object or substance. This energy depends on the position of the object. Every object possesses a potential energy if it is placed above or below the datum plane. The datum plane is an imaginary plane where the height of an object is considered to be zero from the ground. The potential energy at the datum plane is always zero.