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An aluminium bush is to be fitted over a brass rod. At 20^oC, inner diameter of aluminium ring is 5.00 cm and brass rod has a diameter of 5.05 cm.
$(Given, α_{Al} = 24 \times {10^{- 6}}^{\circ} C^{- 1}, α_{brass} = 19 \times {10^{- 6}}^{\circ} C^{- 1})$ . To make the assembly, which of the following operations cannot be performed?

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Both aluminium ring and brass rod can be cooled using liquid nitrogen

Aluminium ring is heated above 437^oC

Brass rod is cooled

Both aluminium ring and brass rod can be heated $(α_{Al} > α_{brass})$

answer is B, C, D.

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Detailed Solution

For option (1)

$L_{2} = L_{1} (1 + αΔT)$

$5 .050 = 5 (1 + 24 \times 10^{- 6} \times ΔT) \Rightarrow T = 437^{\circ} C$ .

For options (2) and (4), temperature below -273^oC is required which is unattainable.
For option (3), temperature of 3000^oC is required which is above melting point of aluminium.

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