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The density of a uniform steel wire of m...

The density of a uniform steel wire of mass `1.6 xx 10^(-2) kg`, and length 2.5 m is `8 xx 10^(3) kg//m^(3)`. When it is loaded by 8kg, it elongates by 1.25 mm. If `g = 10 m//s^(2)`, then the Young's modulus of the material of the wire is

A

`1.5 xx 10^(11) N//m^(2)`

B

`2 xx 10^(11) N//m^(2)`

C

`1.75 xx 10^(11) N//m^(2)`

D

`1.5 xx 10^(12) N//m^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`d = (m)/(V) = (m)/(A xx L)`
`:. A = (m)/(d xx L) = (1.6 xx 10^(-2))/(8 xx 10^(3) xx 2.5) = 8 xx 10^(-7) m^(2)`
`:. Y = (F xx L)/(A xx e) = (8 xx 10 xx 2.5)/(8 xx 10^(-7) xx 1.25 xx 10^(-3))`
`= 2 xx 10^(11) N//m^(2)`
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