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  4. A thin wire of length ℓ when heated to a certain temperature increases its length by 1 %. A sheet of the same material of area 2ℓ × ℓ is heated to the same temperature then percentage increase in area will be:-

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Q. A thin wire of length $\ell $ when heated to a certain temperature increases its length by $1\%.$ A sheet of the same material of area $2\ell \times \ell $ is heated to the same temperature then percentage increase in area will be:-

NTA AbhyasNTA Abhyas 2020

Solution:

$\frac{\Delta \ell }{\ell }\times 100=1$
Area $=2\ell \times \ell $
$\frac{\Delta A}{A}=\frac{\Delta \ell }{\ell }+\frac{\Delta \ell }{\ell }$
$\Rightarrow \frac{\Delta A}{A}\times 100=\frac{2 \times \Delta \ell }{\ell }\times 100$
$=2\%$