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JEE PHYSICS MCQ: MECHANICAL PROPERTIES OF SOLIDS

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The Young’s modulus of brass and steel are

10 \times {10^{10}}\,\mathrm{N}{\mathrm{m}^{ - 2}}\,\,\mathrm{and}\,\,2 \times {10^{11}}\,\mathrm{N}{\mathrm{m}^{ - 2}}

respectively. A brass wire and a steel wire of the same length are extended by

\mathrm{1 mm}

under the same force. The radii of the brass and steel wires are

{R_B}\,\,and\,\,{R_S}

respectively. Then

View answer and explanation

Correct option: B

{R_S} = \frac{{{R_B}}}{{\sqrt 2 }}

Option B (

{R_S} = \frac{{{R_B}}}{{\sqrt 2 }}

) is correct because the radius is inversely proportional to the square root of Young's modulus when other parameters are constant.

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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.