A thin copper wire of length L increases in length by 1 % when heated from temperature T1 to T2 . The percentage change in the area when a thin copper plate having dimensions 2L× L is heated from T1 to T2 is

Question

A thin copper wire of length L increases in length by 1 % when heated from temperature T1 to T2 . The percentage change in the area when a thin copper plate having dimensions 2L× L is heated from T1 to T2 is (A) 2 % (B) 1 % (C) 4 % (D) 3 %

Tardigrade Admin · Accepted Answer

Fractional charge in length (Δ l/l)=α .Δ θ Fractional change in area (Δ A/A)=β .Δ θ But β =2α ∴ (Δ A/A)=(2 α )Δ θ (Δ A/A)=2((Δ l/l)) (Δ A/A)=2(1 %)=2 %

Q. A thin copper wire of length $L$ increases in length by $1%$ when heated from temperature $T_{1}$ to $T_{2}$ . The percentage change in the area when a thin copper plate having dimensions $2 L \times L$ is heated from $T_{1}$ to $T_{2}$ is

$2%$

$1%$

$4%$

$3%$

Fractional charge in length
$\frac{Δ l}{l} = α .Δ θ$
Fractional change in area
$\frac{Δ A}{A} = β .Δ θ$
But $β = 2 α$
$∴ \frac{Δ A}{A} = (2 α) Δ θ$
$\frac{Δ A}{A} = 2 (\frac{Δ l}{l})$
$\frac{Δ A}{A} = 2 (1%) = 2%$

Q. A thin copper wire of length L increases in length by 1% when heated from temperature T1​ to T2​ . The percentage change in the area when a thin copper plate having dimensions 2L×L is heated from T1​ to T2​ is

2%

1%

4%

3%