A fireman wants to slide down a rope. The breaking load for the rope is 3/4th of the weight of the man. With what minimum acceleration sholud the fireman slide down? Acceleration due to gravity is g.

Options

A. zero
B. `g/4`
C. `(3g)/4`
D. `g/2`

Answer

To solve the problem, we need to analyze the forces acting on the fireman as he slides down the rope. Let's break it down step by step.

### Step 1: Identify the Forces Acting on the Fireman
The fireman has two main forces acting on him:
1. The gravitational force (weight) acting downward, which is \( W = mg \).
2. The tension in the rope acting upward, which has a maximum value equal to the breaking load of the rope.

### Step 2: Determine the Breaking Load of the Rope
According to the problem, the breaking load of the rope is \( \frac{3}{4} \) of the weight of the fireman. Therefore, we can express the breaking load as:
\[ T = \frac{3}{4} mg \]
where \( T \) is the tension in the rope.

### Step 3: Apply Newton's Second Law
When the fireman slides down with an acceleration \( a \), we can apply Newton's second law. The net force acting on the fireman can be expressed as:
\[ F_{\text{net}} = mg - T \]
According to Newton's second law, this net force is also equal to the mass times the acceleration:
\[ F_{\text{net}} = ma \]
Thus, we can set up the equation:
\[ mg - T = ma \]

### Step 4: Substitute the Tension in the Equation
Now we substitute the expression for tension \( T \) into the equation:
\[ mg - \frac{3}{4}mg = ma \]

### Step 5: Simplify the Equation
Now, simplify the left side:
\[ mg - \frac{3}{4}mg = \frac{1}{4}mg \]
So we have:
\[ \frac{1}{4}mg = ma \]

### Step 6: Solve for Acceleration \( a \)
Now, we can solve for \( a \) by dividing both sides by \( m \):
\[ \frac{1}{4}g = a \]
Thus, the minimum acceleration \( a \) with which the fireman should slide down is:
\[ a = \frac{g}{4} \]

### Final Answer
The minimum acceleration with which the fireman should slide down is:
\[ \boxed{\frac{g}{4}} \]