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JEE PHYSICS MCQ: MECHANICAL PROPERTIES OF SOLIDS

1 Medium

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A metal bar of length

L

and area of cross-section

A

is clamped between two rigid supports. For the material of the rod, Young's modulus is

Y

and coefficient of linear expansion is

\alpha

. If the temperature of the rod is increased by

\Delta t^{\circ} \mathrm{C}

, the force exerted by the rod on the support is

View answer and explanation

Correct option: B

Y A \alpha \Delta t

Option B (

Y A \alpha \Delta t

) is correct because the force is calculated using Young's modulus, area, coefficient of linear expansion, and temperature change.

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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.