A stone is accelerated upwards by a cord whose breaking strength is three times the weight of the stone. The maximum acceleration with which the stone can be moved up without breaking the cord is

Options

A. g
B. 2 g
C. 3 g
D. 4g

Answer

To solve the problem, we will analyze the forces acting on the stone and apply Newton's second law of motion.

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Stone:**
- The weight of the stone (W) acting downwards: \( W = mg \)
- The tension in the cord (T) acting upwards.

2. **Determine the Maximum Tension:**
- The breaking strength of the cord is given as three times the weight of the stone. Therefore:
\[ T_{\text{max}} = 3W = 3mg \]

3. **Apply Newton's Second Law:**
- According to Newton's second law, the net force acting on the stone is equal to the mass of the stone multiplied by its acceleration (a):
\[ T - mg = ma \]

4. **Substitute the Maximum Tension:**
- We substitute \( T_{\text{max}} \) into the equation:
\[ 3mg - mg = ma \]

5. **Simplify the Equation:**
- Simplifying the left side gives:
\[ 2mg = ma \]

6. **Solve for Maximum Acceleration (a):**
- We can cancel the mass (m) from both sides (assuming \( m \neq 0 \)):
\[ 2g = a \]
- Thus, the maximum acceleration with which the stone can be moved upwards without breaking the cord is:
\[ a_{\text{max}} = 2g \]

### Final Answer:
The maximum acceleration with which the stone can be moved upwards without breaking the cord is \( 2g \).

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