A 50kg man with 20 kg load on his head climbs up 20 steps of 0.25 m height each. The work done in climbing is

Options

A. 5 J
B. 350 J
C. 100 J
D. 3430 J

Answer

To solve the problem of calculating the work done by a man climbing 20 steps with a load on his head, we can follow these steps:

### Step 1: Determine the total height climbed
The height of each step is given as 0.25 meters, and there are 20 steps. Therefore, the total height (h) climbed can be calculated as:

\[ h = \text{number of steps} \times \text{height of each step} = 20 \times 0.25 \, \text{m} = 5 \, \text{m} \]

### Step 2: Calculate the total mass being lifted
The man has a mass of 50 kg and is carrying a load of 20 kg. Thus, the total mass (m) being lifted is:

\[ m = \text{mass of man} + \text{mass of load} = 50 \, \text{kg} + 20 \, \text{kg} = 70 \, \text{kg} \]

### Step 3: Use the work done formula
The work done (W) against gravity when lifting an object is given by the formula:

\[ W = m \cdot g \cdot h \]

where:
- \( m \) is the total mass (70 kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( h \) is the height climbed (5 m).

### Step 4: Substitute the values into the formula
Now, substituting the values into the work done formula:

\[ W = 70 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 5 \, \text{m} \]

### Step 5: Calculate the work done
Calculating the above expression:

\[ W = 70 \cdot 9.8 \cdot 5 = 3430 \, \text{J} \]

### Final Answer
The work done in climbing is \( 3430 \, \text{J} \).

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