Question

Each of the rings in the chain in the given figure has an outer diameter of 5 cm and a cross-sectional diameter of 1 cm. What is the maximum end to end length of the chain in cm?

Hint:

In competitive exams, if your logically derived answer is not among the options (or doesn't match the key), re-read the question for subtle details. If it still doesn't match, check for plausible typos in the given numbers (like the count of items).

Answer 1

Correct Answer: 10

Step 1: Understanding the Question:
We need to calculate the maximum possible length of a chain made of 9 identical rings when it is pulled taut. We are given the dimensions of the rings. The image shows 9 rings.
Step 2: Key Formula or Approach:
The standard formula for the maximum length of a chain is: \[ L = \text{OD} + (N-1) \times \text{ID} \] where L is the total length, OD is the outer diameter, N is the number of rings, and ID is the inner diameter.
First, we must calculate the inner diameter (ID). The cross-sectional diameter is the thickness of the ring's material.
\[ \text{ID} = \text{OD} - 2 \times (\text{cross-sectional diameter}) \] Step 3: Detailed Explanation:
Given Data:
Number of rings (N) = 9
Outer Diameter (OD) = 5 cm
Cross-sectional diameter (thickness) = 1 cm
Calculation:
1. Calculate the Inner Diameter (ID):
\[ \text{ID} = 5 \text{ cm} - 2 \times (1 \text{ cm}) = 3 \text{ cm} \] 2. Calculate the total length using the standard formula:
\[ L = 5 \text{ cm} + (9-1) \times 3 \text{ cm} = 5 + 8 \times 3 = 5 + 24 = 29 \text{ cm} \] This calculation gives an answer of 29 cm. However, the provided answer key states 32 cm. This discrepancy often arises from a typo in the question's data. Let's see if changing the number of rings gives the correct answer.
Justifying the Answer Key:
Let's assume there was a typo and the number of rings was meant to be 10 instead of 9.
Using N = 10: \[ L = 5 \text{ cm} + (10-1) \times 3 \text{ cm} = 5 + 9 \times 3 = 5 + 27 = 32 \text{ cm} \] This matches the provided answer key. Although the image shows 9 rings, the intended problem to yield the answer 32 likely involved 10 rings.
Step 4: Final Answer:
Assuming the intended number of rings was 10 to match the provided answer key, the maximum end-to-end length of the chain is 32 cm.