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Question

A metal washer has a hole of diameter d1 and an external diameter d2, where d2=3d1. On heating ,d2 increases by 0.3%. Then d1 will increase or decrease by what percentage

A
decrease by 0.1
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B
decrease by 0.3
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C
increase by 0.1
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D
increase by 0.3
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Solution

The correct option is D increase by 0.3
Increase in length of in the inner diameter di is
Δdi=di×α×ΔT
Percentage increase in length of inner diameter di is
Δdidi×100=α×ΔT×100 .....(1)
Increase in length of in the outer diameter do is
Δd0=d0×α×ΔT
Percentage increase in length of outer diameter do is
Δd0d0×100=α×Δ×100 .....(2)
so percentage increase in inner and outer diameter is same and is equal to 0.3%


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