If a pump is capable of lifting 5000kg of water through a vertical height of 60m in 15 min, the power of the pump is

Analyze the question: We need the power of a pump that lifts 5000 kg of water through 60 m in 15 minutes.

Concept: Power is the rate of doing work:

P = Work done / Time = mgh / t

The work done by the pump is the gain in gravitational potential energy of the water.

Solution:

• Mass, m = 5000 kg
• Height, h = 60 m
• Time, t = 15 min = 15 × 60 = 900 s
• g = 10 m/s²

Work done = mgh = 5000 × 10 × 60 = 3,000,000 J = 3.0 × 10⁶ J

Power = 3,000,000 / 900 = 3333.3 W ≈ 3.3 × 10³ J/s

(If g = 9.8 m/s², P = 3267 W ≈ 3.3 × 10³ W, which gives the same option.)

Check against the options:

• A. 2.25 × 10⁵ J/s (too large)
• B. 2.5 × 10⁴ J/s (too large)
• C. 3.3 × 10³ J/s (matches)
• D. 3.3 × 10² J/s (too small)

Tip: Always convert minutes to seconds before using the power formula. A common mistake is to divide by 15 instead of 900, which gives an answer 60 times too large. Also, remember that 1 W = 1 J/s, so the options written in js⁻¹ are simply watts.