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In an experiment, brass and steel wires ...

In an experiment, brass and steel wires of length 1 m each with areas of cross section `1mm^(2)` are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is, [Given, the Young’s Modulus for steel and brass are, respectively, `120 xx 10^(9) N//m^(2) and 60 xx 10^(9) N//m^(2)`

A

`1.8 xx 10^(6) N//m^(2)`

B

`4.0 xx 10^(6) N//m^(2)`

C

`1.2 xx 10^(6) N//m^(2)`

D

`8 xx 10^(6) N//m^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`Y_("eq") = ("Stress")/(((Delta l)/(l_(eq))))`
`(2l)/(Y_(eq) A)= (l)/(Y_(1)A) + (l)/(Y_(2)A)`
`Y_(eq) = (2Y_(1) Y_(2))/(Y_(1) + Y_(2)) = (2 xx 120 xx 10^(9) xx 60 xx 10^(9))/(180 xx 10^(9))`
`Y_(eq)= 80 xx 10^(9)`
Stress `= Y_(eq) (Delta l)/(l_(eq))= (80 xx 10^(9) xx 2 xx 10^(-4))/(2m)= 8 xx 10^(6) N//m^(2)`
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