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Question

The volume of a metal sphere increased by 0.24 % when its temperature is raised by 40C. The coefficient of linear expansion of metal is

A
2×105C1
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B
4×105C1
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C
5×105C1
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D
8×105C1
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Solution

The correct option is A 2×105C1
We know,
Final volume V=V0(1+γΔT)
where γ is coefficient of volumetric expansion
ΔVV0=γΔT
% Change in volume ΔVV0×100=γΔT×100
0.24=γ×40×100
γ=6×105C1

Also,we know,
α=γ3
where α is coefficient of linear expansion
α=6×105C13
=2×105C1

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