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The length of a wire is 1.0 m and the ar...

The length of a wire is `1.0 m` and the area of cross-section is `1.0 xx 10^(-2) cm^(2)`. If the work done for increase in length by `0.2 cm` is 0.4 joule, then Young's modulus of the material of the wire is

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
`l=1m, A= 1 xx 10^(-6) m^(2), Delta l= 0.2 xx 10^(-2)`
`W= (1)/(2) xx` Stress `xx` Strain `xx` Volume
`W= (1)/(2) xx Y ("strain")^(2) xx Al rArr W= (1)/(2) Y (Delta l^(2)A)/(l)`
`Y= (2Wl)/(A(Delta l)^(2))= (2 xx 0.4 xx 1)/(10^(-6) xx (0.2 xx 10^(-2))^(2)) = 2 xx 10^(11) N//m^(2)`
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