A boy of mass 40 kg climbs up a flight of 30 steps each 20 cm high in 2 min and a girl of mass 30 kg does the same in 1.5 min. Compare : (i) the work done, and (ii) the power developed by them (g = 10 m `s^(-2)`)

Explanation

While climbing, both the boy and the girl have to do work against their force of gravity.
Force of gravity of boy
`F_(1)=m_(1)g=40xx10=400N`
Force of gravity of girl
`F_(2)=m_(2)g=30xx10=300N`
Total height climed up
h=number of steps `xx` height of each step (i)Work done by the boy
`W_(1)=F_(1)xxh=300xx6=1800J`
Work done by the girl
`W_(2)=F_(2)xxh=300xx6=1800J`
`W_(1):W_(2)`=2400:1800 =4:3
(ii)Power developed =`("Work done")/("Time taken")`
Here ,`t_(1)`=2min=120 s,`t_(2)`=1.5 min =90 s
Power developed by boy
`P_(1)=(W_(2))/(t_(2))=(1800J)/(90s)=20W`
`P_(1):P_(2)=20:20=1:1`
Alternative :(i)since height climbed is same
`(W_(1))/(W_(2))=(m_(1)gh)/(m_(2)gj)=(m_(1))/(m_(2))=(40)/(30)=(4)/(3)`
(ii) `(P_(1))/(P_(2))=(W_(1)//t_(1))/(W_(2)//t_(2))=(W_(1))/(W_(2))xx(t_(2))/(t_(1))=(4)/(3)xx(1.5)/(2)=(1)/(1)`