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A piece of metal weighs 46 g in air. When it is immersed in a liquid of specific gravity 1.24 at $27 ° C,$ it weighs 30 g. When the temperature is raised to $42 ° C$ , the metal piece weighs 30.5 g. If the specific gravity of the liquid at $42 ° C$ is 1.20, the coefficient of linear expansion of the metal is

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$2.4 \times 10^{- 6} / ° C$

$2.3 \times 10^{- 5} / {}^{\circ}C$

$2.2 \times 10^{- 6} / {}^{\circ}C$

None of these

answer is B.

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Detailed Solution

Change in weight = Upthrust (F)

where,

$30 = 46 - V \times 1.24 \Rightarrow V = \frac{16}{1.24} c m^{3} A l s o 30.5 = 46 - \frac{16}{1.24} (1 + \times 15 γ_{m}) \times 1.2 \Rightarrow α_{m} = 2.3 \times 10^{- 5} p e r d e g r e e c e n t i g r a d e$

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