Question

A train of mass \(10^6 \, \text{kg}\) is moving at a constant speed of \(108 \, \text{km/h}\). If the frictional force acting on it is \(0.5 \, \text{N per 100 kg}\), then the power of the train is

• A. 300 kW
• B. 150 kW
• C. 75 kW
• D. 225 kW

Hint:

Always convert all units to SI before applying formulas. Power due to force at constant speed is calculated as \(P = F \cdot v\).

Answer 1

The Correct Option is B

Step 1: Given data
Mass of the train, \(m = 10^6 \, \text{kg}\)
Speed, \(v = 108 \, \text{km/h} = \frac{108 \times 1000}{3600} = 30 \, \text{m/s}\)
Frictional force per 100 kg = 0.5 N
Step 2: Find total frictional force
Total frictional force \(F = \left(\frac{10^6}{100}\right) \times 0.5 = 10^4 \times 0.5 = 5000 \, \text{N}\)
Step 3: Power is given by
\[ P = F \cdot v = 5000 \times 30 = 150000 \, \text{W} = 150 \, \text{kW} \]
Step 4: Choose the correct option
So, the power of the train is \(\boxed{150 \, \text{kW}}\), which corresponds to option (2).