Q85 / 90 · JEE Main 2021 (01 Sep Shift 2) · Physics

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

Correct answer: 8

Solution

Thermal force $F = A y α Δ T$

$F = (10 \times 10^{- 4}) \times (2 \times 10^{11}) (10^{- 5}) (400)$
$F = 8 \times 10^{5} N$
$\Rightarrow x = 8$

Hence, the correct answer is 8.