A long chain having 100 identical steel links is to be pulled from its two ends by a force of 3000 Newtons. The chain is elongated by adding another 50 links to it. Which one of the following is the correct statement?

Options

A. The force induced in each link will be equal to 20 Newtons.
B. The force induced in each link will be equal to 30 newtons.
C. The force induced in each link will be equal to 3000 newtons.
D. The force induced in each link cannot be determined unless its dimensions are given.

Answer

To solve the problem, we need to analyze the situation step by step.

### Step 1: Understand the Problem
We have a chain made of 100 identical steel links, and it is being pulled from both ends by a force of 3000 Newtons. When another 50 links are added, we need to determine the force induced in each link.

### Step 2: Calculate the Total Number of Links
Initially, there are 100 links. After adding 50 more links, the total number of links becomes:
\[ \text{Total Links} = 100 + 50 = 150 \]

### Step 3: Calculate the Force Induced in Each Link
The total force applied to the chain is 3000 Newtons. Since the force is distributed equally among all the links, we can find the force in each link by dividing the total force by the total number of links:
\[ \text{Force per link} = \frac{\text{Total Force}}{\text{Total Links}} = \frac{3000 \text{ N}}{150} \]

### Step 4: Perform the Calculation
Now, we perform the calculation:
\[ \text{Force per link} = \frac{3000}{150} = 20 \text{ N} \]

### Step 5: Analyze the Options
Now we can analyze the options given in the question:
1. The force induced in each link will be equal to 20 Newtons. (This is true)
2. The force induced in each link will be equal to 30 Newtons. (This is false)
3. The force induced in each link will be equal to 3000 Newtons. (This is false)
4. The force induced in each link cannot be determined unless its dimensions are given. (This is false)

### Conclusion
The correct statement is that the force induced in each link will be equal to 20 Newtons.

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