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:-

Question

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:- (A) 4 % (B) 2.5 % (C) 2 % (D) 1.5 %

Tardigrade Admin · Accepted Answer

(Δ ℓ /ℓ )× 100=1 Area =2ℓ × ℓ (Δ A/A)=(Δ ℓ /ℓ )+(Δ ℓ /ℓ ) ⇒ (Δ A/A)× 100=(2 × Δ ℓ /ℓ )× 100 =2 %

Q. 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 $2 ℓ \times ℓ$ is heated to the same temperature then percentage increase in area will be:-

$4%$

$2.5%$

$2%$

$1.5%$

$\frac{Δ ℓ}{ℓ} \times 100 = 1$
Area $= 2 ℓ \times ℓ$
$\frac{Δ A}{A} = \frac{Δ ℓ}{ℓ} + \frac{Δ ℓ}{ℓ}$
$\Rightarrow \frac{Δ A}{A} \times 100 = \frac{2 \times Δ ℓ}{ℓ} \times 100$
$= 2%$

Q. 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:-

4%

2.5%

2%

1.5%