A man raises a box of mass 50 kg to a height of 2 m in 2 minutes, whil

1.	A man raises a box of mass 50 kg to a height of 2 m in 2 minutes, while another man raises the same box to the same height in 5 minutes. Compare:(i) the work done and(ii) the power developed by them.
Answer» (i) Work done in raising a 50kg mass to a height 2m against the force of gravity is: W = mg × h = mgh Hence both men will do the same amount of work. Hence, work done by A/work done by B = mgh/mgh = 50 x 10 x 2/50 x 10 x 2 = 1/1 = 1: 1 (ii) First man A takes 2 minutes to raise 50 kg mass Second man B takes 5 minutes to raise 50 kg mass. Power developed by man A = work done/Time taken mgh/t = 50 x 10 x 2J/120S = 25/3W Power developed by man B = work done/Time taken = mgh/t = 50 x 10 x 2J/5 x 60s = 10/3 W Power developed α 1/time taken Power developed by A/Power developed by B = (25/3)/(10/3) = 25/10 = 5/2 = 5 : 2

A man raises a box of mass 50 kg to a height of 2 m in 2 minutes, while another man raises the same box to the same height in 5 minutes. Compare:(i) the work done and(ii) the power developed by them.

Answer»

(i) Work done in raising a 50kg mass to a height 2m against the force of gravity is:

W = mg × h = mgh

Hence both men will do the same amount of work. Hence,

work done by A/work done by B = mgh/mgh = 50 x 10 x 2/50 x 10 x 2 = 1/1 = 1: 1

(ii) First man A takes 2 minutes to raise 50 kg mass

Second man B takes 5 minutes to raise 50 kg mass.

Power developed by man A = work done/Time taken mgh/t = 50 x 10 x 2J/120S = 25/3W

Power developed by man B = work done/Time taken = mgh/t = 50 x 10 x 2J/5 x 60s = 10/3 W

Power developed α 1/time taken

Power developed by A/Power developed by B = (25/3)/(10/3) = 25/10 = 5/2 = 5 : 2