A glass window is to be fit an aluminium frame. The temperature on the working day is 40°C and the glass window measure exactly 20 cm X 30 cmαglass =9×10−6/∘C,αaluminium=24×10−6/∘C. The size of the aluminium frame is ____, so that there is no stress on the glass in winter even if the temperature drops to 0°C ?

No stress ⇒L11=L21&B11=B21….(1)L11=L11+α1(−40)….(2a)L21=L21+α2(−40)….(2b)B11=B11=α1(−40)….(2c)B21=B21+α2(−40)….(3d)From (1) & (2) equationsL2=20×1-9×10-6×401-24×10-6×40=20.012 cm B2=30×1-9×10-6×401-24×10-6×40= 30.01 cm

A glass window is to be fit an aluminium frame. The temperature on the working day is 40°C and the glass window measure exactly 20 cm X 30 cmαglass =9×10−6/∘C,αaluminium=24×10−6/∘C. The size of the aluminium frame is ____, so that there is no stress on the glass in winter even if the temperature drops to 0°C ?

No stress ⇒L11=L21&B11=B21….(1)L11=L11+α1(−40)….(2a)L21=L21+α2(−40)….(2b)B11=B11=α1(−40)….(2c)B21=B21+α2(−40)….(3d)From (1) & (2) equationsL2=20×1-9×10-6×401-24×10-6×40=20.012 cm B2=30×1-9×10-6×401-24×10-6×40= 30.01 cm

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A glass window is to be fit an aluminium frame. The temperature on the working day is 40°C and the glass window measure exactly 20 cm X 30 cm $[α_{glass} = 9 \times 10^{- 6} /^{\circ} C, α_{alu min ium} = 24 \times 10^{- 6} /^{\circ} C]$ . The size of the aluminium frame is ____, so that there is no stress on the glass in winter even if the temperature drops to 0°C ?

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20.012 cm X 30.01 cm

10 cm X 20 cm

30 cm X 20 cm

15 cm X 30 cm

answer is A.

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Detailed Solution

$No stress \Rightarrow L_{1}^{1} = L_{2}^{1} & B_{1}^{1} = B_{2}^{1} \dots . (1)$

$\begin{aligned} L_{1}^{1} = L_{1} [1 + α_{1} (- 40)] \dots . (2 a) \\ L_{2}^{1} = L_{2} [1 + α_{2} (- 40)] \dots . (2 b) \\ B_{1}^{1} = B_{1} [1 = α_{1} (- 40)] \dots . (2 c) \\ B_{2}^{1} = B_{2} [1 + α_{2} (- 40)] \dots . (3 d) \end{aligned}$
From (1) & (2) equations