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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

`96 xx 10^(-3) m`

B

`19.2 xx 10^(-5) m`

C

`9.4 cm`

D

`9.6 m`

Text Solution

Verified by Experts

The correct Answer is:
c
Due to own weight,
`Delta I = (mgl)/(2AY) = ((IA rho)gl)/(2AY) = (I^(2) rho g)/(2Y) = ((8)^(2) (1.5 xx 10^(3))(9.8))/(2 xx 5 xx 10^(6))`
`= 9.4 xx 10^(-2) m = 9.4 cm`
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Knowledge Check

  • The Young's modulus of a rubber string 8 cm long and density 1.5kg//m^(3) is 5xx10^(8)N//m^(2) is suspended on the ceiling in a room. The increase in length due to its own weight will be-

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  • For silver Young's modulus is 7.5 xx 10^(10) N//m^(2) and Bulk modulus is 11 xx 10^(10) N//m^(2) . Its poisson's ratio will be

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    `0.39`
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