Question

500 litres of water is raised from the first floor of a house at height 4 m to its third floor at height 12 m. If density of water is $1kg{l}^{-1}$ then the change in potential energy is (take $g=10m{s}^{-2}$):

• A. $4\times {10}^{4}J$
• B. $-4\times {10}^{4}J$
• C. $2\times {10}^{4}J$
• D. $-2\times {10}^{4}J$

Answer 1

The correct option is A $4\times {10}^{4}J$

Given, volume of water$=500l$,
acceleration due to gravity, $g=10m{s}^{-2}$,
density of water $=1kglitr{e}^{-1}$,
first floor height $h_1=4m$
and third floor height $h_2=12m$
Let the mass of water be $m$
Mass of water, m= Volume of water$\times$density of water$=500\times 1=500kg$
As the height of water above the ground increases ($h_2>h_1$), the potential energy of water will increase.
Increase in potential energy$=mg(h_2-h_1)=500\times 10\times (12-4)=4\times {10}^{4}J$
Therefore, the increase in potential energy will be $4\times {10}^{4}J$.