A steel rod $y = 2 \times {10^{11}}\,N/{m^2}$ and $\alpha = {10^{ - 5}}/\,{\,^ \circ }C$ of length 1m and area of cross section $1\,c{m^2}$ is heated from ${0^ \circ }C$ to ${200^ \circ }C$ with out being allowed to extend or bend. What is the tension produced in the rod?

JEE PHYSICS MCQ: MECHANICAL PROPERTIES OF SOLIDS

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A steel rod

y = 2 \times {10^{11}}\,N/{m^2}

and

\alpha = {10^{ - 5}}/\,{\,^ \circ }C

of length 1m and area of cross section

1\,c{m^2}

is heated from

{0^ \circ }C

{200^ \circ }C

with out being allowed to extend or bend. What is the tension produced in the rod?

View answer and explanation

Correct option: D

4 \times {10^4}\,N

Option D (

4 \times {10^4}\,N

) is correct because the tension produced in the rod is calculated using the formula involving Young's modulus, area, coefficient of linear expansion, and change in temperature.

More Questions from MECHANICAL PROPERTIES OF SOLIDS

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A wire is stretched under a force. If the wire suddenly snaps the temperature of the wire The increases in length is

l

of a wire of length

L

by the longitudinal stress. Then the stress is proportional to A steel wire of length

l

and cross sectional area

\mathrm{A}

is stretched by

1 \mathrm{~cm}

under a given load. When the same load is applied to another steel wire of double its length and half of its cross section area, the amount of stretching (extension) is Assertion: From the relation

Y=\frac{F l}{A \Delta l},

we can say that, if length of a wire is doubled, its Young's modulus of elasticity will also becomes two times.

Reason: Modulus of elasticity is a material property. A wire can be broken by applying a load of 200 N. The force required to break another wire of the same length and same material, but double in diameter, is Assertion(A): If radius of cylindrical wire is doubled, then this wire can bear four times stress.

Reason(R): By doubling the radius, area of cross-section will become four times.