a boy of mass 40 kg runs up a flight of 50 steps , each of 10 cm high, in 5 sec. find the power developed by the boy ?

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Solution

Dear Student

Mass of the boy (m₁) = 40 kg
Mass of the girl (m₂) = 50 kg
Time taken by boy (t₁) = 50 sec
Time taken by girls (t₂) = 40 sec
Height of each stair = 0.15 m
acceleration due to gravity = 10 m/s²
Number of steps = 50
Total height moved by him (h) = 50 x 0.15 m = 7.5 m
(a) Work done by Boy in moving against gravitational pull (W₁) = m₁gh = 40 x 10 x 7.5= 3000 J
Work done by girls in moving against the gravitational pull (W₂) = m₂gh = 50 x 10 x 7.5 = 3750 J
$R a t i o o f W_{1} a n d W_{2} = \frac{W_{1}}{W_{2}} = \frac{3000}{3750} = 0.8$
$(b) P o w e r d e v e l o p e d b y b o y = \frac{W o r k d o n e}{T i m e} = \frac{3000}{50} = 60 P o w e r d e v e l o p e d b y g i r l s = \frac{W o r k d o n e}{T i m e} = \frac{3750}{40} = 93.75 R a t i o o f P o w e r d e v e l o p e d = \frac{P o w e r d e v e l o p e d b y b o y}{P o w e r d e v e l o p e d b y g i r l s} = \frac{60}{93.75} = 0.64$

Regards

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