Question

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

1. the work, and
2. power developed by them.

Answer 1

Mass of bucket m = 20 kg

∵ 1 cm³ of water = 1g

∵ 1000 cm³ = 1 Lit. = 1 kg

Height to which bucket is raised h = 20 m

(i) Work done by boy and father = mgh

= 20 × 9.8 × 20

= 3920 J

∵ Work done is independent of time taken

∴ Ratio of work done = 1 : 1

(ii) Power developed is

`"P"_"boy"/"P"_"father" = ("W"/"t"_"boy")/("W"/"t"_"father") = (3920/180s)/(3920/120s) = 120/180`

`therefore "P"_"boy"/"P"_"father" = 2/3 = 2 : 3`

Power developed by boy : Power developed by father = 2 : 3