Question

A tank of size \[10\,m \times 10\,m \times 10\,m\] 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 Use the mass formula given below and find the mass of the tank. Substitute the obtained mass value and the acceleration due to gravity given in the potential energy formula, to find the value of the potential energy of the tank.

Useful formula
(1) The formula for the mass is given by
$m = \rho V$
Where $m$ is the mass of the tank, $\rho $ is the density of the tank and $V$ is its volume.
(2) The formula of the potential energy is given as
$P = mgh$
Where $P$ is the potential energy of the tank, $g$ is the acceleration due to gravity and the $h$ is the height of the tank.

Complete step by step solution
It is given that the
Dimensions of the tank is \[10\,m \times 10\,m \times 10\,m\]
Acceleration due to gravity, $g = 10\,m{s^{ - 2}}$
From the size of the tank, its volume is calculated as follows,
$V = 10 \times 10 \times 10 = 1000\,{m^3}$
Using the formula of the mass,
$m = \rho V$
$m = 1000 \times 1000 = {10^6}Kg$
The potential energy acts at the midway of the tank. Hence the height is considered as $5\,m$.
Using the formula of the potential energy,
$P = mgh$
Substituting the known values in it,
$P = {10^6} \times 10 \times 5$
By simplification of the above equation, we get
$P = 5 \times {10^7}\,J$
Hence the potential energy of the tank filled with the water is obtained as $5 \times {10^7}\,J$ .

Thus the option (A) is correct.

Note In the above solution, it is substituted that the density of the water is $1000$ in order to find the value of the mass. The potential energy asked in this problem is the energy due to rest or storage of the water in the tank but the kinetic energy is used when movement.