A sphere is accelerated upwards with the help of a cord whose braking strength is five times its weight. The maximum acceleration with which the sphere can move up without cord breaking is :-

Options

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

Answer

To solve the problem, we need to analyze the forces acting on the sphere and apply Newton's second law of motion. Here’s a step-by-step solution:

### Step 1: Identify the forces acting on the sphere
The forces acting on the sphere are:
- The weight of the sphere (mg) acting downwards.
- The tension in the cord (T) acting upwards.

### Step 2: Understand the breaking strength of the cord
The problem states that the breaking strength of the cord is five times the weight of the sphere. Therefore, we can express the maximum tension (T_max) as:
\[ T_{max} = 5mg \]

### Step 3: Apply Newton's second law
According to Newton's second law, the net force acting on the sphere is equal to the mass of the sphere multiplied by its acceleration (a):
\[ T - mg = ma \]
Where:
- T is the tension in the cord,
- mg is the weight of the sphere,
- a is the acceleration of the sphere.

### Step 4: Substitute the maximum tension into the equation
Since we want to find the maximum acceleration before the cord breaks, we can substitute \( T \) with \( T_{max} \):
\[ 5mg - mg = ma \]

### Step 5: Simplify the equation
Now, simplify the equation:
\[ 4mg = ma \]

### Step 6: Solve for acceleration (a)
To find the acceleration \( a \), divide both sides by \( m \):
\[ 4g = a \]

### Conclusion
The maximum acceleration with which the sphere can move up without the cord breaking is:
\[ a = 4g \]

### Final Answer
The maximum acceleration is \( 4g \).

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