JEE PHYSICS MCQ: MECHANICAL PROPERTIES OF SOLIDS

1 Medium

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Understanding +4 | -1

Assertion: Every wire is like a spring, whose spring constant,

K \propto \frac{1}{l}

where

l

is length of wire.

Reason: It follows from the relation

K=\frac{Y A}{l}

View answer and explanation

Correct option: A

If both Assertion and Reason are true and the Reason is correct explanation of the Assertion

Option A (If both Assertion and Reason are true and the Reason is correct explanation of the Assertion) is correct because the spring constant is inversely proportional to the length of the wire, as derived from the given relation.

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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.