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A thick rope of rubber of density 1.5 xx...

A thick rope of rubber of density `1.5 xx 10^(3) kg m^(-3)` and Young's modulus `5 xx 10^(6) Nm^(-2)`, 8 m in length, when hung from ceiling of a room, the increases in length due to its own weight is

A

`9.4 xx 10^(-2) m`

B

`19.2 xx 10^(-2) m`

C

`9.4 xx 10^(-3) m`

D

`9.4m`

Text Solution

Verified by Experts

The correct Answer is:
A
If A is the area of cross section and l is the length of rope, then mass of rope ,m ` = Al rho `
As the weight of the rope acts at the mid point of the rope
so `Y = (mg)/(A) xx ((l/2))/(Delta l)`
`Delta l = (mgl)/(2AY) = (Al rho g l)/(2AY) = (g rho l^2)/(2Y)`
` Delta l = (9.8 xx 1.5 xx 10^3 xx 8^2)/(2 xx 5 xx 10^6) = 9.4 xx 10^(-2) m`
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