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Question

When the temperature of a copper coin is raised by 800 C, its diameter increases by 0.2%

A
percentage rise in the area of a face is 0.4%
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B
percentage rise in the thickness is 0.4%
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C
percentage rise in the volume is 0.6%
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D
coefficient of linear expansion of copper is 0.25×104/0C
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Solution

The correct options are
B percentage rise in the area of a face is 0.4%
C percentage rise in the volume is 0.6%
D coefficient of linear expansion of copper is 0.25×104/0C
Percentage increase in diameter is given by
ll×100=αT×100=0.2%--------(1)
αT×100=0.2%
α=0.002T×100=0.00280×100=0.25×104/0C
Now, percentage change in Area is given by,
AA×100=βT×100
Putting values from equation (1):
AA×100=2αT×100
AA×100=2(0.2)AA×100=0.4%
0.4% is the percentage rise in Area.
VV×100=γT×100=3×αT×100
VV×100=3(0.2)AA×100=0.6%
0.6% is the percentage rise in volume.

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