A porter lifts a luggage of 15 kg from ground and puts it on his head 2.0 m above the ground. The work done by porter on the luggage is: [Take g = 10 m/s²]

Question

Accepted Answer

To determine the work done by the porter on the luggage, we use the formula for work done against gravity:

$$ \text{Work done (W)} = \text{Force (F)} \times \text{Displacement (d)} $$

In this scenario, the force exerted by the porter is equal to the weight of the luggage, which can be calculated using the formula:

$$ \text{Force (F)} = \text{mass (m)} \times \text{acceleration due to gravity (g)} $$

Given:
- Mass of the luggage, $ m = 15 \, \text{kg} $
- Acceleration due to gravity, $ g = 10 \, \text{m/s}^2 $
- Displacement, $ d = 2.0 \, \text{m} $

First, calculate the force:

$$ F = 15 \, \text{kg} \times 10 \, \text{m/s}^2 = 150 \, \text{N} $$

Next, calculate the work done:

$$ W = F \times d = 150 \, \text{N} \times 2.0 \, \text{m} = 300 \, \text{Nm} $$

Therefore, the work done by the porter on the luggage is 300 Nm, which corresponds to Option 1.

**Explanation for why other options are incorrect:**

- **Option 2 (30 Nm):** This value is incorrect because it significantly underestimates the work done. The calculation of work done involves multiplying the force (150 N) by the displacement (2 m), resulting in 300 Nm, not 30 Nm.

- **Option 3 (600 Nm):** This value is incorrect because it overestimates the work done. The correct calculation yields 300 Nm, not 600 Nm. The error likely arises from mistakenly doubling the correct work done value.

- **Option 4 (3 Nm):** This value is incorrect because it drastically underestimates the work done. The work done is calculated as 300 Nm, not 3 Nm. This option is off by a factor of 100, indicating a significant miscalculation.

In conclusion, the correct answer is Option 1 (300 Nm), as it accurately reflects the work done by the porter in lifting the luggage 2 meters above the ground.