Question

A two kilowatt motor pumps out water from a well 10 meter deep. The quantity of water pumped out per hour is ( g = 10 $m/s^2$)

• A. $72\times {10}^2$ kg
• B. $72\times {10}^3$ kg
• C. $72\times {10}^4$ kg
• D. $72\times {10}^5$ kg

Answer 1

The correct option is B $72\times {10}^3$ kg

$\text{Step 1: Work done}$

Work done will be equal to change in potential energy of system in pumping out the water from $10m$ deep well.

Let $m$ be the mass of water that is pumped out per sec.

$2kW$ motor pump means that $2kJ$ work is done in $1$ sec.

$W=mgh$

$\Rightarrow 2000J=m\times 10m{s}^{-2}\times 10m$

$\Rightarrow m=20kg$

So, Quantity of water pumped out per sec, $m=20kg$

$\text{Step 2: Quantity of of water pumped out per hour}$

$\therefore \text{Quantity of water that is pumped out per hour}=m\times 3600$

$=20kg\times 3600=72\times {10}^{3}kg$

Hence option(B) is correct.