A steel rod with $\mathrm{y}=2.0 \times 10^{11} \mathrm{Nm}^{-2}$ and $\alpha=10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ of length 4 m and area of cross-section 10 $\mathrm{cm}^{2}$ is heated from $0^{\circ} \mathrm{C}$ to $400^{\circ} \mathrm{C}$ without being allowed to extend. The tension produced in the rod is $x \times 10^{5} \mathrm{~N}$ where the value of $x$ is ______.

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Heat & Thermodynamics

A steel rod with

y = 2.0 \times 1 0^{11} Nm^{- 2}

and

α = 1 0^{- 5}^{\circ} C^{- 1}

of length 4 m and area of cross-section 10

cm^{2}

is heated from

0^{\circ} C

40 0^{\circ} C

without being allowed to extend. The tension produced in the rod is

x \times 1 0^{5} N

where the value of

x

is ______.

Answer: 8

Solution

Preventing expansion sets up a thermal stress whose force is

F = Y A α Δ T

. With

Y = 2.0 \times 1 0^{11} N/m^{2}

A = 10 cm^{2} = 1 0^{- 3} m^{2}

α = 1 0^{- 5}^{\circ} C^{- 1}

and

Δ T = 400^{\circ} C

F = 2.0 \times 1 0^{11} \times 1 0^{- 3} \times 1 0^{- 5} \times 400 = 8 \times 1 0^{5} N

, so

x = 8

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Integer answer

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