A thin wire of length when heated to a certain temperature increases its length by 1%. A sheet of the same material of area 20l x l is heated to the same temperature then percentage increase in area will be:

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A thin wire of length when heated to a certain temperature increases its length by 1%. A sheet of the same material of area 20l x l is heated to the same temperature then percentage increase in area will be:

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2.5%

1.5%

answer is C.

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Detailed Solution

$\frac{Δ ℓ}{ℓ} \times 100 = 1$

$Area = 2 ℓ \times ℓ$

$\frac{ΔA}{A} = \frac{Δℓ}{ℓ} + \frac{Δℓ}{ℓ}$

$\Rightarrow \frac{ΔA}{A} \times 100 = \frac{2 \times Δℓ}{ℓ} \times 100$

= 2%

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