Question

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

• A. 2dgh
• B. dgha
• C. 2dgh²a
• D. dgh²a

Answer 1

Answer: (A)

2dgh

Answer 2

Potential energy of liquid column in first situation

$= V d g \frac { h } { 2 } + V d g \frac { h } { 2 }$ = $V d g h = a h d g h$ $= d g h ^ { 2 } a$

[As centre of mass of liquid column lies at height $\frac { h } { 2 }$]

Potential energy of the liquid column in second situation $= V d g \left( \frac { 2 h } { 2 } \right) = ( A \times 2 h ) d g h = 2 d g h ^ { 2 } a$

Work done pumping = Change in potential energy

= $2 d g h ^ { 2 } a - d g h ^ { 2 } a = d g h ^ { 2 } a$.