An object is resting at the bottom of two strings which are inclined at an angle of `120^(@)` with each other. Each string can withstand a tension of 20 N. The maximum weight of the object that can be sustained without breaking the string is

Options

A. 10 N
B. 20 N
C. `20sqrt(2)`
D. 40 N

Explanation

To solve the problem, we need to determine the maximum weight of the object that can be sustained by the two strings without breaking them. Here’s a step-by-step solution:

### Step 1: Understand the Setup
We have two strings inclined at an angle of \(120^\circ\) with each other, supporting an object at the bottom. Each string can withstand a maximum tension of \(20 \, \text{N}\).

### Step 2: Identify Forces Acting on the Object
The forces acting on the object include:
- The gravitational force (weight) acting downwards, denoted as \(W\) (or \(mg\)).
- The tension forces in the strings acting upwards at an angle.

### Step 3: Analyze the Tension Components
Since the strings are inclined, we need to resolve the tension into its components. Let \(T\) be the tension in each string. The angle between each string and the vertical is \(60^\circ\) (since \(120^\circ\) is the angle between the two strings, each string makes a \(60^\circ\) angle with the vertical).

### Step 4: Calculate the Vertical Components of Tension
The vertical component of the tension from each string can be calculated as:
\[ T_{vertical} = T \cos(60^\circ) \]
Since \(\cos(60^\circ) = \frac{1}{2}\), we have:
\[ T_{vertical} = T \cdot \frac{1}{2} \]

### Step 5: Total Vertical Force from Both Strings
Since there are two strings, the total vertical force supporting the weight of the object is:
\[ F_{total} = 2T \cos(60^\circ) = 2T \cdot \frac{1}{2} = T \]

### Step 6: Set Up the Equation
For the object to be in equilibrium (not moving), the total upward force must equal the downward force (weight of the object):
\[ W = T \]

### Step 7: Substitute the Maximum Tension
Given that each string can withstand a maximum tension of \(20 \, \text{N}\), we substitute \(T = 20 \, \text{N}\):
\[ W = 20 \, \text{N} \]

### Conclusion
The maximum weight of the object that can be sustained without breaking the strings is:
\[ \boxed{20 \, \text{N}} \]