Power required by a boy of mass 30 kg to run up a staircase of 40 steps in 10 seconds is'
(Height of each step is 15 cm)
(Take `g = 10 m//s^(2)`)

Options

A. 1800 Watt
B. 180 Watt
C. 18000 Watt
D. 18 Watt

Explanation

To find the power required by a boy of mass 30 kg to run up a staircase of 40 steps in 10 seconds, we can follow these steps:

### Step 1: Calculate the total height climbed
The height of each step is given as 15 cm. To find the total height for 40 steps, we can use the formula:

\[ \text{Total Height} = \text{Number of Steps} \times \text{Height of Each Step} \]

Converting the height of each step to meters:
\[ \text{Height of Each Step} = 15 \text{ cm} = 0.15 \text{ m} \]

Now, calculate the total height:
\[ \text{Total Height} = 40 \times 0.15 = 6 \text{ m} \]

### Step 2: Calculate the weight of the boy
The weight (force due to gravity) can be calculated using the formula:
\[ \text{Weight} = \text{mass} \times g \]
Where \( g = 10 \text{ m/s}^2 \) (acceleration due to gravity).

Substituting the values:
\[ \text{Weight} = 30 \text{ kg} \times 10 \text{ m/s}^2 = 300 \text{ N} \]

### Step 3: Calculate the work done
Work done against gravity when climbing the stairs can be calculated using the formula:
\[ \text{Work Done} = \text{Force} \times \text{Displacement} \]

Substituting the values:
\[ \text{Work Done} = 300 \text{ N} \times 6 \text{ m} = 1800 \text{ J} \]

### Step 4: Calculate the power required
Power is defined as the work done per unit time. The formula for power is:
\[ \text{Power} = \frac{\text{Work Done}}{\text{Time}} \]

Substituting the values:
\[ \text{Power} = \frac{1800 \text{ J}}{10 \text{ s}} = 180 \text{ W} \]

### Final Answer
The power required by the boy to run up the staircase is **180 Watts**.

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