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))

A boy of mass 40 kg climbs up a flight of 30 steps each 20 cm high in

1.	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))
Answer» Solution : 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)`