Question

Two army persons A and B each of weight of 500 N climb up a rope through a height of 10 m. A takes 20 s while B takes 40 s to achieve this task. What is ratio of the powers of person A and B? *​

Answer 1

Answer:

The ratio of powers of A and B = 2: 1  

Explanation:

 Power = \frac{W}{t} = \frac{F.S}{t}

Where , Fa = 500N    S = 10m

           Fb = 500N    ta = 20s , tb = 40s

Pa = \frac{Fa.S}{ta} = \frac{500 \times 10}{20} = 250 watts

Pa = \frac{Fa.S}{tb} = \frac{500 \times 10}{40} = 125 watts

\frac{Pa}{Pb} = \frac{250}{125} = \frac{2}{1} = 2 : 1

Answer 2

Given:

Force of A, Fa = 500 N

Force of B, Fb = 500 N

Displacement, s = 10 m

Time taken by A, Ta = 20 s

Time taken by B, Tb = 40s.

To Find:

Ratio of the powers, Pa:Pb

Solution:

Power = Work done / Time taken

Work done = Force × Displacement

Work done by A, Wa = Fa × s

= 500 × 10 = 5000 J

Work done by B, Wb = Fb × s

= 500 × 10 = 5000 J

Power of A, Pa = 5000 / 20 = 250 W

Power of B, Pb = 5000 / 40 = 125 W

Pa / Pb = 250 / 125 = 2/1

Ratio = 2:1

The ratio of the powers of person A and B is 2:1