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Question
A boy of weight 40 kgf climbs up the 15 steps, each 15 cm high in 10 s and a girl of weight 20 kgf does the same in 5 s. Compare:
- the work done, and
- the power developed by them. Take g = 10 N kg-1.
Solution
Weight of boy = 40 kgf
No. of steps = 15; Each = 15 cm; Time = 10 sec
Force of gravity on boy -
F1 = m1g = 40 × 10 = 400 N
Force of gravity on girl -
F2 = m2g = 20 × 10 = 200 N
Total height climbed (h) = 15 × 15 = 225 cm = 2.25 m
(i) Work done by boy -
W1 = F1 × h = 400 × 2.25 = 900 J
Work done by Girl -
W2 = F2 × h = 200 × 2.25 = 450 J
W1 : W2 = `900/450 = 2/1`
W1 : W2 = 2 : 1
(ii) Power = `"work done"/"Time taken"`
t1 = 10 sec; t2 = 5 sec
P1 [Boy] = `(900 " J")/(10 " s")` = 90 W
P2 [Girl] = `(450 " J")/(5 " s")` = 90 W
P1 : P2 = 90 : 90 = 1 : 1
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