How can you lower a 100 kg body from the roof of a house using a cord with a breaking strength of 80 kg weight without breaking the rope? (1 kg weight = gN)

Options

A. `1.96 m//s^(2)` downwards
B. `9.8 m//s^(2)` downwards
C. `4.9 m//s^(2)` downwards
D. `19.6 m//s^(2)` downwards

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 kg weight without breaking the rope, we can follow these steps:

### Step 1: Understand the Forces Acting on the Body
The weight of the body (W) can be calculated using the formula:
\[ W = mg \]
where:
- \( m = 100 \, \text{kg} \) (mass of the body)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

Thus, the weight of the body is:
\[ W = 100 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 980 \, \text{N} \]

### Step 2: Determine the Breaking Strength of the Cord
The breaking strength of the cord is given as 80 kg weight. To convert this to Newtons:
\[ \text{Breaking Strength} = 80 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 784 \, \text{N} \]

### Step 3: Set Up the Equation of Motion
When lowering the body, the forces acting on it are:
- Downward force due to weight (W = 980 N)
- Upward force due to the tension in the cord (T = Breaking Strength = 784 N)

Using Newton's second law, we can express the net force (F_net) acting on the body:
\[ F_{\text{net}} = W - T \]
\[ F_{\text{net}} = 980 \, \text{N} - 784 \, \text{N} = 196 \, \text{N} \]

### Step 4: Calculate the Acceleration of the Body
According to Newton's second law:
\[ F_{\text{net}} = ma \]
where \( m \) is the mass of the body. Rearranging gives us:
\[ a = \frac{F_{\text{net}}}{m} \]
Substituting the values:
\[ a = \frac{196 \, \text{N}}{100 \, \text{kg}} = 1.96 \, \text{m/s}^2 \]

### Step 5: Conclusion
The acceleration of the body while being lowered is \( 1.96 \, \text{m/s}^2 \) downwards. This means that the body can be lowered safely without breaking the rope, as the tension in the rope does not exceed its breaking strength.