Question

A boy takes $3$ minutes to lift a $20$ litre water bucket from a $20m$ deep well, while his father does it in $2$ minutes. (a) Compare: (i) the work and (ii) power developed by them. (b) How much work each does? Take density of water $={10}^{3}kg{m}^{-3}$ and $g=9.8N{kg}^{-1}$

Answer 1

(a) $\text{Step 1: Work done :}$

(i) Work done doesn't depend upon time. So work done by both of them would be the same.

Work done will be an equal change in potential energy in lifting the water bucket from $20m$ deep well.

Work done in both cases $=mgh$

$=20\times 9.8\times 20=400\times 9.8=3920J$

$\text{Step 2: Power developed :}$

(ii)Power developed by the boy: $=\frac{\text{work done}}{\text{time taken by the boy}}=\frac{3920}{3\times 60}=21.78W$

Power developed by the father: $=\frac{\text{work done}}{\text{time taken by the father}}=\frac{3920}{2\times 60}=32.67W$

(b)Each does work $=mgh=3920J$