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ICSE Class 10 Physics Question 21 of 27

Solved Sample Paper 3 — Question 9

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9
Question

Question 6(iii)

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.

Answer

(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 = Work donetime\dfrac{\text{Work done}}{\text{time}}

Power developed by first man (P1) = 1000120\dfrac{1000}{120} = 253\dfrac{25}{3}

Power developed by second man (P2) = 1000300\dfrac{1000}{300} = 103\dfrac{10}{3}

Ratio of power developed by the two men :

P1P2=253103=253×310=52\dfrac{P_1}{P_2} = \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