A 40 kg girl runs up a flight of stairs having a rise of 5 m in 4 s. The power developed by her will be ________. (take g = 10 m/s²)
- A.100 W
- B.200 W
- C.500 W
- D.2000 W
Correct answer
Explanation
The correct answer is C, 500 W. The work done against gravity is mgh = 40 × 10 × 5 = 2000 joule, and power is work divided by time, so 2000 ÷ 4 = 500 watt.
Power is the rate of doing work, measured in watt, where one watt is one joule per second. In climbing stairs the useful work is the gain in potential energy, mgh, where only the vertical rise counts and the length of the staircase does not matter. If the same girl ran up in 2 seconds the work would be the same 2000 joule but the power would double to 1000 watt, which shows that power depends on how fast the work is done.
Option A is wrong because 100 W comes from dividing by the wrong quantity. Option B is wrong because 200 W would need 10 seconds. Option D is wrong because 2000 is the work in joule, not the power in watt.
Exam tip: work = mgh, power = work ÷ time, and one horsepower is about 746 watt.
Practice Questions
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