Question

A steel wire of uniform cross section of $1sqmm$ is heated to ${70}^{o}C$ and stretched by tying it two ends rigidly. Calculate the change in tension on the wire when temperature falls from ${70}^{o}C$ to ${35}^{o}C.$
(Co-efficient of linear expansion of steel $=1.1\times {10}^{-5}{C}^{-1}$ and Young's modulus is $2.0\times {10}^{11}$ Pa.)

• A. $55N$
• B. $88N$
• C. $66N$
• D. $77N$

Answer 1

The correct option is D $77N$

we know that Young's modulus is given as

$Y=\left(F/A\right).\left(dL/L\right)$

or

$Y=\left(F/A\right).\alpha dT$

thus, tension will be

$F=Y.A.\alpha dT$

here,

$Y=2.0\times 1011N{m}^2$

$A={1mm}^2={10}^6{m}^2$

$\alpha =1.1\times {10}^{-5o}C$

$dT=70\circ C-35\circ C$

so,

$F=2\times 1011\times {10}^6\times 1.1\times {10}^5\times 35$

thus,

$F=77N$