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Two metal rods A and B have same difference of 60 cm length at all temperatures. If the coefficients of linear expansions of the metals of A and B respectively are $18 \times {10^{- 6}}^{o} C^{- 1}$ and $27 \times {10^{- 6}}^{o} C^{- 1}$ then the initial lengths of the rods A and B respectively are

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120 cm and 80 cm

180 cm and 120 cm

160 cm and 100 cm

240 cm and 180 cm

answer is B.

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Detailed Solution

for the given condition

$l_{1} α_{1} = l_{2} α_{2}$

$l \times 27 = (l + 60) 18$

l=120 cm and other is 180 cm

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