A steel chain consists of 50 links connected to each other. The chain is pulled by applying force F at each of its ends. What is the magnitude of force induced in each link?

Options

A. `F//50`
B. F
C. 50 F
D. `F//25`

Answer

To solve the problem of finding the magnitude of force induced in each link of a steel chain consisting of 50 links, we can follow these steps:

### Step 1: Understand the Setup
We have a steel chain with 50 links, and a force \( F \) is applied at both ends of the chain. Each link is connected to the next, and we need to determine the force experienced by each link.

**Hint:** Visualize the chain and the forces acting on it. Consider how the links are connected.

### Step 2: Analyze One Link
Let’s focus on the first link of the chain. When the force \( F \) is applied at both ends, the first link is being pulled from the left by force \( F \) and is connected to the second link on the right.

**Hint:** Draw a free body diagram of the first link to see the forces acting on it.

### Step 3: Apply Newton's First Law
Since the chain is in equilibrium (not accelerating), the net force acting on the first link must be zero. This means that the force pulling it from the left (which is \( F \)) must be balanced by the force exerted by the second link (let's call this force \( F' \)).

**Hint:** Remember that if the net force is zero, then the forces acting on the object must be equal.

### Step 4: Set Up the Equation
From the analysis, we have:
\[ F - F' = 0 \]
This implies:
\[ F' = F \]

**Hint:** Think about how the forces balance each other out.

### Step 5: Generalize for All Links
This reasoning applies to every link in the chain. Each link experiences the same force \( F \) being transmitted through the chain. Therefore, the force induced in each link is equal to the force applied at the ends of the chain.

**Hint:** Consider that all links are identical and experience the same conditions.

### Conclusion
The magnitude of the force induced in each link of the chain is \( F \).

### Final Answer
The force induced in each link is \( F \).

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