Question

A boy takes 3 minutes to lift a 20-liter water bucket from a 20 m deep well, while his father does it in 2 minutes. Compare

(i) the work and

(ii) power developed by them.

Take density of water=${10}^{3}kg{m}^{-3}andg=9.8Nk{g}^{-1}$.

Answer 1

Given data

The volume of water = 20 L = $\frac{20}{1000}=0.02m^3$

So we can write,

Mass of water = Density $\times$ Volume = 1000$\times$0.02 = 20 kg

(i)

Work done by boy = $m\times g\times h$ = 20$\times$9.8$\times$20 = 3920 J
Work done by father = $m\times g\times h$ = 20$\times$9.8$\times$20=3920 J

Comparison of work done

3920 : 3920 = 1:1

(ii)

Time taken by boy = 3 min = 180 s
Time taken by father = 2 min = 120 s

Power developed by the boy = $\frac{3920}{180}=21.78W$

Power developed by the father = $\frac{3920}{120}=32.67W$

Comparison of the power developed = $\frac{3920}{180}:\frac{3920}{120}$ =2:3