An Indian rubber cord L metre long and area of cross-section A metr{e^2} is suspended vertically. De

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8.Mechanical Properties of Solids

hard

An Indian rubber cord $L$ metre long and area of cross-section $A$ $metr{e^2}$ is suspended vertically. Density of rubber is $D$ $kg/metr{e^3}$ and Young's modulus of rubber is $E$ $newton/metr{e^2}$. If the wire extends by $l$ metre under its own weight, then extension $l$ is

A

${L^2}Dg/E$

B

${L^2}Dg/2E$

C

${L^2}Dg/4E$

D

$L$

Solution

(b) $F=m g=(A L D) g$

stress $=\frac{F}{A}=L D g$

strain $=\frac{l}{L / 2}$

Stress $=E \times$ strain

$L D g=E \times \frac{l}{L / 2}$

$l=\frac{L^{2} D g}{2 E}$

Standard 11

Physics

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