Question

A liquid of density $d$ is pumped by pump P from situation (i) to situation (ii) as shown in the figure. If the cross section of each of the vessel is $a$, then the work done in pumping (neglecting friction effects) is:

• A. $dg{h}^{2}a$
• B. $2dgh$
• C. $dgha$
• D. $2dg{h}^{2}a$

Answer 1

The correct option is A $dg{h}^{2}a$

The distance of the center of mass of liquid in a single column from the bottom is at half the height of the column.

Thus gravitational potential energy of both columns before pumping=$\left(dah\right)g\frac{h}{2}+\left(dah\right)g\frac{h}{2}$

$=dg{h}^{2}a$

Total gravitational potential energy of liquid column after pumping=$\left(da\right(2h\left)\right)g\frac{2h}{2}$

$=2dg{h}^{2}a$

Thus work done in pumping$=dg{h}^{2}a$