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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:
- the work, and
- power developed by them.
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Solution
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
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