Question

A cubical vessel of height $2$m is full of water. The work done in pumping the water out of the vessel is?

• A. $72.3$kJ
• B. $78.4$kJ
• C. $64.5$kJ
• D. $57.9$kJ

Answer 1

The correct option is B $78.4$kJ

Let l be the length of cube.
So, mean height of water from the ground is
$h=\frac{l}{2}$
Mass of water in cubical vessel is
$m=v\rho =l^3\rho$
So, work done is pumping out the water will be
$w=mgh=mg\frac{l}{2}$
$=l^3\rho \cdot g\frac{l}{2}=\frac{pg{l}^4}{2}$
$=\frac{1}{2}\left(1000\right)\times \left(9.8\right)\cdot (2{)}^4$
$=4900\times 16=78400J=78.4$kJ.