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Two rings made of metals A and B with ring A having a larger diameter, are placed concentrically leaving an annular gap. The thermal expansion coeffic
Question

Two rings made of metals A and B with ring A having a larger diameter, are placed concentrically leaving an annular gap. The thermal expansion coefficients of the two metals are CA and CB . Identify the correct statement(s) from the following.
A. The gap will decrease if CA < CB.

B. The gap will remain the same if CA = CB.

C. The gap will increase if CA < CB.

A.

Only A

B.

A and B

C.

Only C

D.

A, B and C

Correct option is D

Given:

Outer ring = A (larger diameter)

Inner ring = B

Gap = distance between outer ring and inner ring

Cₐ = coefficient of expansion of ring A

Cᵦ = coefficient of expansion of ring B

Concept:

Increase in size ∝ coefficient of thermal expansion

If outer ring expands more → gap increases

If inner ring expands more → gap decreases

If both expand equally → gap remains same

Solution:

Case 1:

Cₐ < Cᵦ

Inner ring expands more than outer ring.

Gap decreases.

Statement A is correct.

Case 2:

Cₐ = Cᵦ

Both rings expand equally.

Gap remains same.

Statement B is correct.

Case 3:

Cₐ > Cᵦ

Outer ring expands more than inner ring.

Gap increases.

Statement C is correct.

Final Answer: (d) A, B and C

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