A boy weighing 40 kgf climbs up a stair of 30 steps each 20 cm high in 4 minute and a girl weighing 30 kgf does the same in 3 minutes. Compare(with ratio):- (1) The work done by them (2) The power developed by them ( I require an answer at the earliest, I have not received an answer for this query from over 3 days.)

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Solution

Dear Student.
$W o r k d o n e = F o r c e \times d i s p l a c e m e n t . H e r e i n b o t h c a s e s w o r k i s d o n e a g i n s t t h e g r a v i t y . W . D_{b o y} = 40 \times 9.81 \times H (H t o t a l d i s \tan c e t r a v e l l e d) . W . D_{g i r l} = 30 \times 9.81 \times H d i s \tan c e t r a v e l l e d i s s a m e i n b o t h t h e c a s e . \frac{W . D_{b o y}}{W . D_{g i r l}} = \frac{40 \times 9.81 \times H}{30 \times 9.81 \times H} = \frac{4}{3} \frac{W . D_{b o y}}{W . D_{g i r l}} = \frac{4}{3} I n s e c o n d p a r t w e a r e s u p p o s e d t o f i n d t h e r a t i o o f t h e r e p P o w e r = \frac{w o r k d o n e}{t i m e t a k e n} P_{b o y} = 40 \times 9.81 \times H / 4 = 98.1 H P_{g i r l} = 30 \times 9.81 \times H / 3 = 98.1 H \frac{P_{b o y}}{P_{g i r l}} = 1 W h i c h m e a n s t h a t p o w e r b y b o y a n d g i r l a r e s a m e .$
Regards.

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