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Question

On heating a uniform metallic cylinder, length increases by 3%. The area of cross - section of its base will increase by

A
1.5 %
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B
3 %
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C
9 %
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D
6 %
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Solution

The correct option is D 6 %
The relation between superficial (or areal coefficient) and linear coefficient for a solid object is given by
β=2α
Given, percentage increase in length for a small change in temperature (α×ΔT)=3 %
Percentage increase in area of cross-section for small change in temperature (β×ΔT)=2 (α×ΔT)=2×3=6 %

Thus, Area of cross-section increases by 6 %.
Hence, option (d) is the correct answer.

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