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The coefficients of linear expansion of P and Q are α₁ and α₂ respectively. If the coefficient of cubical expansion of ‘Q’ is three times the coefficient of superficial expansion of P, then which of the following is true ?

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${\alpha _2} = 2{\alpha _1}$

${\alpha _1} = 2{\alpha _2}$

${\alpha _2} = 3{\alpha _1}$

${\alpha _1} = 3{\alpha _2}$

answer is A.

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Detailed Solution

Coefficient of cubical expansion $\gamma = 3\alpha.$

Coefficient of superficial expansion $\beta = 2\alpha .$

$\therefore 3{\alpha _2} = 3 \times 2{\alpha _1} \Rightarrow {\alpha _2} = 2{\alpha _1}$

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