NHT0015 16. A metal rod is heated increasing its temperature
by 10°C. The fractional change in its length is
1 *10-4. If a plate of same metal is heated raising
its temperature by 5°C, the fractional change in
its area will be .-
(1) 1 x 10-4
(2) 0.5 x 10-4
(3) 2 x 10-4
(4) 3 x 10-4​

(1) 1×10⁻⁴

Explanation:

From the question,

α = (ΔL/L)/(ΔT) Equation 1

Where α = linear expansivity of the metal plate, ΔL/L = Fractional change in Length, ΔT = Rise in temperature.

Given: ΔL/L = 1×10⁻⁴, ΔT = 10°C

Substitute these values into equation 1

α  = 1×10⁻⁴/10

α = 1×10⁻⁵ °C⁻¹ .

β = (ΔA/A)/ΔT Equation 2

Where β = Coefficient of Area expansivity, ΔA/A = Fractional change in area.

make ΔA/A the subject of the equation

ΔA/A = β×ΔT Equation 3

But,

β = 2α Equation 4

Substitute equation 4 into equation 3

ΔA/A = 2α×ΔT Equation 5

Given: ΔT = 5°C, α = 1×10⁻⁵ °C⁻¹

Substitute into equation 5

ΔA/A = ( 2)×(1×10⁻⁵)×(5)

ΔA/A  = 10×10⁻⁵

ΔA/A  = 1×10⁻⁴

Hence the right option is (1) 1×10⁻⁴

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