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Q.

If the coefficient of real expansion γr is 1% more then coefficient of apparent expansion, linear expansion coefficient of the material is

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a

large frac {gamma_r}{303}

b

large frac {100gamma_r}{101}

c

large frac {101gamma_r}{300}

d

large frac {101gamma_r}{100}

answer is A.

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Detailed Solution

Given that large gamma_r=frac {101}{100}gamma_aRightarrow gamma_a=frac {100}{101}gamma_r
We have large gamma_r=gamma_a+3alpha_gRightarrow gamma_r=frac {100}{101}gamma_r+3alpha_g
large gamma_rleft [ 1-frac {100}{101} right ]=3alpha_gRightarrow alpha_g=frac {gamma_r}{303}

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If the coefficient of real expansion γr is 1% more then coefficient of apparent expansion, linear expansion coefficient of the material is