JEE PHYSICS MCQ: MECHANICAL PROPERTIES OF SOLIDS

1 Medium

1 of 1

Application +4 | -1

14.5 \mathrm{~kg}

mass, fastened to the end of a steel wire of unstretched length

1 \mathrm{~m}

, is whirled in a vertical circle with an angular velocity of

2 \mathrm{~rev} / \mathrm{s}

at the bottom of the circle. The cross-sectional area of the wire is

0.065 \mathrm{~cm}^2

. The elongation of the wire when the mass is at the lowest point of its path is;

\text {[ } Y_{\text {steel }}=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2 \text { ] }

View answer and explanation

Correct option: C

1.87 \mathrm{~mm}

Option C (

1.87 \mathrm{~mm}

) is correct because it is the elongation calculated using Young's modulus, the force due to gravity and centripetal acceleration, and the given dimensions of the wire.

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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.