A man weighing 50 kg, climbs up a staircase carrying a bag of 10 kg on bis head. The staircase has 15 steps and each steps has a height of 20 cm. What is the power required by the man, if he takes 10 seconds to climb the staircase?

Options

A. 120w
B. 150.5W
C. 176.4w
D. 200W

Explanation

To find the power required by the man to climb the staircase, we need to follow these steps:

### Step 1: Calculate the total weight of the man and the bag.
The weight of the man is 50 kg, and the weight of the bag is 10 kg.

\[ \text{Total weight} = \text{Weight of man} + \text{Weight of bag} = 50 \, \text{kg} + 10 \, \text{kg} = 60 \, \text{kg} \]

### Step 2: Calculate the total height climbed.
Each step has a height of 20 cm, and there are 15 steps.

\[ \text{Total height} = \text{Number of steps} \times \text{Height of each step} = 15 \times 20 \, \text{cm} = 300 \, \text{cm} = 3 \, \text{m} \]

### Step 3: Calculate the gravitational potential energy gained.
The gravitational potential energy (PE) gained can be calculated using the formula:

\[ \text{PE} = \text{mass} \times g \times \text{height} \]

Where:
- \( g \) (acceleration due to gravity) is approximately \( 9.81 \, \text{m/s}^2 \).

Substituting the values:

\[ \text{PE} = 60 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 3 \, \text{m} \]
\[ \text{PE} = 60 \times 9.81 \times 3 = 1769.8 \, \text{J} \]

### Step 4: Calculate the power required.
Power is defined as the work done (or energy transferred) per unit time. The formula for power (P) is:

\[ P = \frac{\text{Work done}}{\text{Time}} = \frac{\text{PE}}{\text{Time}} \]

Given that the time taken is 10 seconds:

\[ P = \frac{1769.8 \, \text{J}}{10 \, \text{s}} = 176.98 \, \text{W} \]

### Final Answer:
The power required by the man to climb the staircase is approximately **177 W**.

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