The weight of a person is `60` kg . If he gets `10` calories of heat through food and the efficiency of his body is `28%`, then upto what height he can climb? Take g = `10m s^(-2)`

Options

A. `100` cm
B. `1.96` cm
C. `400` cm
D. `1000` cm

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Convert Calories to Joules
The first step is to convert the heat energy from calories to joules. We know that:
1 calorie = 4.2 joules

Given that the person consumes 10 calories:
\[ \text{Heat energy in joules} = 10 \, \text{calories} \times 4.2 \, \text{joules/calorie} = 42 \, \text{joules} \]

### Step 2: Calculate the Work Done by the Body
The efficiency of the body is given as 28%. This means that only 28% of the energy consumed is converted into useful work. Therefore, the work done (W) can be calculated as:
\[ W = \text{Efficiency} \times \text{Total heat energy} \]
\[ W = 0.28 \times 42 \, \text{joules} = 11.76 \, \text{joules} \]

### Step 3: Use the Work-Energy Principle
According to the work-energy principle, the work done by the person climbing is equal to the gravitational potential energy gained. The potential energy (PE) can be expressed as:
\[ PE = mgh \]
Where:
- \(m\) = mass of the person = 60 kg
- \(g\) = acceleration due to gravity = 10 m/s²
- \(h\) = height climbed (which we need to find)

### Step 4: Set Up the Equation
From the work-energy principle, we can equate the work done to the potential energy:
\[ mgh = W \]
Substituting the values we have:
\[ 60 \, \text{kg} \times 10 \, \text{m/s}^2 \times h = 11.76 \, \text{joules} \]

### Step 5: Solve for Height (h)
Now, we can solve for \(h\):
\[ 600h = 11.76 \]
\[ h = \frac{11.76}{600} = 0.0196 \, \text{m} \]

### Step 6: Convert Height to Centimeters
To convert the height from meters to centimeters, we multiply by 100:
\[ h = 0.0196 \, \text{m} \times 100 = 1.96 \, \text{cm} \]

### Final Answer
The height the person can climb is **1.96 cm**.

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