A body of mass 50 kg and specific gravity force is to be lifted using a rope of breaking strength of 60 kg wt. The acceleration with which it can be pulled up in least interval of time

Options

A. Zero
B. g/2
C. g/4
D. g/5

Answer

To solve the problem, we need to find the maximum acceleration with which a body of mass 50 kg can be lifted using a rope that has a breaking strength of 60 kg wt. Here's the step-by-step solution:

### Step 1: Identify the forces acting on the body
The forces acting on the body are:
- The weight of the body (downward force)
- The tension in the rope (upward force)

### Step 2: Calculate the weight of the body
The weight \( W \) of the body can be calculated using the formula:
\[ W = m \cdot g \]
where:
- \( m = 50 \, \text{kg} \) (mass of the body)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

Calculating the weight:
\[ W = 50 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 490 \, \text{N} \]

### Step 3: Determine the maximum tension in the rope
The breaking strength of the rope is given as 60 kg wt. We need to convert this to Newtons:
\[ T_{\text{max}} = 60 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 588 \, \text{N} \]

### Step 4: Apply Newton's second law
According to Newton's second law, the net force \( F_{\text{net}} \) acting on the body is equal to the mass of the body multiplied by its acceleration \( a \):
\[ F_{\text{net}} = T - W = m \cdot a \]
Rearranging this gives:
\[ T - W = m \cdot a \]

### Step 5: Substitute the known values
Substituting the values we have:
\[ 588 \, \text{N} - 490 \, \text{N} = 50 \, \text{kg} \cdot a \]
This simplifies to:
\[ 98 \, \text{N} = 50 \, \text{kg} \cdot a \]

### Step 6: Solve for acceleration \( a \)
Now, we can solve for \( a \):
\[ a = \frac{98 \, \text{N}}{50 \, \text{kg}} = 1.96 \, \text{m/s}^2 \]

### Conclusion
The maximum acceleration with which the body can be pulled up in the least interval of time is:
\[ \boxed{1.96 \, \text{m/s}^2} \]