At what minimum acceleration should a monkey slide a rope whose breaking strength is `(2)/(3)`rd of its weight?

Options

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

Explanation

To find the minimum acceleration at which a monkey can slide a rope whose breaking strength is \( \frac{2}{3} \) of its weight, we can follow these steps:

### Step 1: Define the variables
Let:
- \( m \) = mass of the monkey
- \( g \) = acceleration due to gravity
- Weight of the monkey, \( W = mg \)
- Maximum tension in the rope, \( T_{\text{max}} = \frac{2}{3} W = \frac{2}{3} mg \)

### Step 2: Write the equation of motion for the monkey
When the monkey is sliding down the rope, the forces acting on it are:
- Weight acting downward: \( mg \)
- Tension acting upward: \( T \)

Using Newton's second law, we can write the equation of motion:
\[ mg - T = ma \]
where \( a \) is the acceleration of the monkey.

### Step 3: Substitute the maximum tension
For the minimum acceleration, we will consider the maximum tension in the rope:
\[ T = T_{\text{max}} = \frac{2}{3} mg \]

Substituting this into the equation of motion gives:
\[ mg - \frac{2}{3} mg = ma \]

### Step 4: Simplify the equation
Now, simplify the left-hand side:
\[ mg - \frac{2}{3} mg = \frac{1}{3} mg \]
Thus, we have:
\[ \frac{1}{3} mg = ma \]

### Step 5: Solve for acceleration \( a \)
Now, divide both sides by \( m \) (assuming \( m \neq 0 \)):
\[ \frac{1}{3} g = a \]

### Conclusion
The minimum acceleration \( a \) at which the monkey can slide down the rope is:
\[ a = \frac{g}{3} \]

### Final Answer
The minimum acceleration required for the monkey to slide down the rope is \( \frac{g}{3} \).

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