How can you lower a 100-kg body from the roof of a house using a cord with a breaking strength of 80 kgf (kilogram force) without breaking the rope ?

Answer

To solve the problem of lowering a 100 kg body from the roof of a house using a cord with a breaking strength of 80 kgf without breaking the rope, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Body:**
- The weight of the body (W) acting downwards:
\[ W = Mg = 100 \, \text{kg} \times g \]
- The tension (T) in the cord acting upwards.

2. **Set Up the Equation of Motion:**
- When the body is lowered with an acceleration \( a \), the net force acting on the body can be expressed using Newton's second law:
\[ Mg - T = Ma \]
- Rearranging this gives:
\[ T = Mg - Ma \]

3. **Substitute Values:**
- Substitute \( M = 100 \, \text{kg} \) into the equation:
\[ T = 100g - 100a \]

4. **Determine the Maximum Tension:**
- The maximum tension (T_max) that the cord can withstand is given by the breaking strength of the cord:
\[ T_{max} = 80 \, \text{kgf} = 80g \]

5. **Set Up the Inequality:**
- To ensure the cord does not break, we need:
\[ T \leq T_{max} \]
- Substituting the expression for T:
\[ 100g - 100a \leq 80g \]

6. **Solve for Acceleration (a):**
- Rearranging the inequality gives:
\[ 100g - 80g \leq 100a \]
\[ 20g \leq 100a \]
\[ a \geq \frac{20g}{100} = \frac{g}{5} \]

7. **Conclusion:**
- To lower the 100 kg body safely without breaking the cord, it should be lowered with an acceleration of \( \frac{g}{5} \).