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Q.

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

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a

2 x 10^-5 $/ {}^{0}C$

b

6 x 10^-5 $/ {}^{0}C$

c

18 x 10^-5 $/ {}^{0}C$

d

1.2 x 10^-5 $/ {}^{0}C$

answer is A.

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Detailed Solution

$α = \frac{γ}{3} = \frac{∆ V}{3 V ∆ T} = \frac{1}{3} (\frac{0.24}{100}) (\frac{1}{40}) = 2 \times 10^{- 5}$

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