If a man raises a box of 50 kg mass to a height of 2 m in 2 min, while the other man raises the same box to the same height in 5 min. Compare

(a) the work done and

(b) the power developed by them.

(a) Work done = force x displacement

Hence, work done is same for both men as both carry 50 kg weight to a height of 2m.

Let the work done by both men be W.

As W = mgh = 50 x 10 x 2 = 1000 J

Hence,

Work done by first man : Work done by second man = 1 : 1

(b) Time taken by first man = 2 min = 2 x 60 secs = 120 secs

Time taken by second man = 5 min = 5 x 60 secs = 300 secs

Power = $\dfrac{\text{Work done}}{\text{time}}$

Power developed by first man (P₁) = $\dfrac{1000}{120}$ = $\dfrac{25}{3}$

Power developed by second man (P₂) = $\dfrac{1000}{300}$ = $\dfrac{10}{3}$

Ratio of power developed by the two men :

$\dfrac{P$1}{P2} = \dfrac{\dfrac{25}{3}}{\dfrac{10}{3}} = \dfrac{25}{3} \times \dfrac{3}{10} = \dfrac{5}{2}

Hence, Ratio of power developed by the two men = 5 : 2