There is some change in length when 33000N tensile force is applied on a steel rod of area of cross section 10^–3m². The change in temperature required to produce the same elongation if the steel rod is heated is (The modulus of elasticity is 3 × 10¹¹N/m² and the coefficient of linear expansion of steel is 1.1 × 10^–5/⁰C)

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10⁰C

20⁰C

0⁰C

15⁰C

answer is C.

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Detailed Solution

Free Thermal expansion Δl = l.α.Δt
By Hookes Law, Δl = Fl/AY
$l α ∆ t = \frac{F l}{A Y}$ and we have F = YAαΔt
33000 = 3 x 10¹¹ x 10^-3 x 1.1 x 10^-5 Δt
Δt = 10⁰C

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