Question

A copper wire of length l increase in length by 0.2% on heating from 20°C to
40°C. Then percentage change in area of a copper plate of dimensions
31 x 21 on heating from 20°C to 40°C is
(A) 0.1 %
(B) 0.2%
(C) 0.4%
(D) 0/6%​

Answer 1

Given : A copper wire of length l increase in length by 0.2 % on heating from 20°C to 40°C.

To find : The percentage change in area of a copper plate of dimension 31 × 21 on heating from 20°C to 40°C.

solution : using formula, $\Delta l=l\alpha\Delta T$

as it is given that , ∆l = 0.2 % of l = 0.002l

so, 0.002l = lα × (40°C - 20°C)

⇒2 × 10¯³ = α × 20

⇒α = 1 × 10¯⁴ /°C

now change in area is given by, ∆A = Aβ∆T

we know, β = 2α

so, ∆A = A2α∆T

⇒∆A/A = 2α∆T = 2 × 10¯⁴/°C × 20°C

= 4 × 10¯³

percentage change in area = ∆A/A × 100

= 4 × 10¯³ × 100

= 0.4 %

Therefore the percentage change in area of copper plate is 0.4 % .

option (C) is correct choice.