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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 pl
Question
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
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Physics
4 years
2021-08-27T05:37:06+00:00
2021-08-27T05:37:06+00:00 1 Answers
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Answers ( )
Answer:
(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