Question

A lift raises 50 passengers of average weight \(600\,\text{N}\) each to a height of \(100\,\text{m}\) in time \(T\). If average power used is \(15\,\text{kW}\), then the value of \(T\) is:

• A. \( 150 \) s
• B. \( 100 \) s
• C. \( 300 \) s
• D. \( 200 \) s

Hint:

Power = Work/Time, where Work = Force × Displacement.
Ensure all units are SI: Convert kilowatts to watts.
Multiply total weight (force) with height to get total work.

Answer 1

The Correct Option is D

Step 1: Compute total work done: Each person exerts \(600\,\text{N}\), so total weight = \(600 \times 50 = 30000\,\text{N}\) Height = \(100\,\text{m} \Rightarrow \text{Work} = 30000 \times 100 = 3 \times 10^6\,\text{J}\) Step 2: Given Power = \(15\,\text{kW} = 15000\,\text{W}\) Use: \( W = P \cdot T \Rightarrow T = \frac{W}{P} = \frac{3 \times 10^6}{15000} = 200\,\text{seconds} \)