A person trying to lose weight by burning fat filts a mass of `10 kg` upto a being of `1m 1000` time . Assume that the potential energy lost each time be lower the mass is dissipated . How much far will be use up considering the work done only when the weight is lifted up ? Far supplies `3.8 xx 10^(7) J` of energy per kg wich is canverted to mechanical energy with `x 20 %` efficiency rate Take ` = 9.8 ms^(-2)`

Options

A. `6.45xx10^(-3)` kg
B. `9.89xx10^(-3)` kg
C. `12.89xx10^(-3)` kg
D. `2.45xx10^(-3)` kg

Answer

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

### Step 1: Calculate the Potential Energy Lost
The potential energy (PE) lost when lifting a mass can be calculated using the formula:
\[ PE = m \cdot g \cdot h \]
where:
- \( m = 10 \, \text{kg} \) (mass)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 1 \, \text{m} \) (height)

Substituting the values:
\[ PE = 10 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 1 \, \text{m} = 98 \, \text{J} \]

### Step 2: Calculate Total Work Done
Since the mass is lifted 1000 times, the total work done (W) is:
\[ W = \text{Number of lifts} \cdot PE = 1000 \cdot 98 \, \text{J} = 98000 \, \text{J} \]

### Step 3: Calculate Energy Supplied by Fat
The energy supplied by burning \( x \) kg of fat is given by:
\[ E = x \cdot 3.8 \times 10^7 \, \text{J/kg} \]

### Step 4: Account for Efficiency
Since only 20% of the energy from fat is converted to mechanical energy, the effective energy available for work done is:
\[ \text{Effective Energy} = 0.2 \cdot E = 0.2 \cdot (x \cdot 3.8 \times 10^7) \]

### Step 5: Set Up the Equation
We set the effective energy equal to the work done:
\[ 0.2 \cdot (x \cdot 3.8 \times 10^7) = 98000 \]

### Step 6: Solve for \( x \)
Now we can solve for \( x \):
\[ x \cdot 3.8 \times 10^7 = \frac{98000}{0.2} \]
\[ x \cdot 3.8 \times 10^7 = 490000 \]
\[ x = \frac{490000}{3.8 \times 10^7} \]
\[ x \approx 0.012897 \, \text{kg} \]

### Final Answer
The amount of fat used up is approximately:
\[ x \approx 0.0129 \, \text{kg} \, \text{or} \, 12.9 \, \text{grams} \]