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Limitation of Dimensional Analysis

A rod of leng...

Question

A rod of length 1000 rom and coefficient of linear expansion $α = 10^{- 4}$ ; 10-4 per degree celsius is placed inhorizontal smooth surface symmetrically between fixed walls separated by 1001 rnm. The Young'smodulus of rod is $10^{11} N / m^{2}$ . If the temperatore is increased by $20^{o} C$ , then the stress developed in the rod is ( in $N / m^{2})$

10^{5}

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10^{8}

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10^{7}

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10^{6}

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Solution

The correct option is B $10^{8}$
$Δ l$ due to temperature rise
$= l α Δ Θ$
$= (1000) (10^{- 4}) (20)$
$= 2 m m$
But I mm is allowed (l000mm to 1001 mm)
$∴ Δ l_{e} = 1 m m$
$S t r e e s = Y \times S t r a i n$
$= (10^{11}) (\frac{1 m m}{1000 m m})$
$= 10^{8} N / m^{2}$

Suggest Corrections

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