The minimum power required to lift a mass of 50 kg up to a vertical distance of 8 m in 10 s is : (Take g = 10 m/s²)
- A.400 W
- B.40 W
- C.50 W
- D.500 W
Correct answer
Explanation
The correct answer is A, 400 W. The work done against gravity is mgh = 50 × 10 × 8 = 4,000 J, and doing it in 10 s needs 4,000 ÷ 10 = 400 W.
Power is the rate of doing work, P = W/t, and its SI unit is the watt (1 W = 1 J/s). Lifting a body at a steady speed means doing work equal to the gain in its potential energy, mgh. The answer is the minimum because any friction or acceleration would need extra energy. For comparison, one horsepower is about 746 W.
B is wrong because 40 W is ten times too small, as if the height were 0.8 m.
C is wrong because 50 W ignores g and the height; it simply repeats the mass.
D is wrong because 500 W would correspond to a height of 10 m, not 8 m.
Exam tip: P = mgh/t; 1 kW = 1,000 W and 1 hp ≈ 746 W.
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