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Question

If the ratio of lengths, radii and Youngs modulii of steel and brass wires in the figure are a, b and c respectively. Then the corresponding ratio of increase in their lengths would be:
293473_4de9a8f7e3ff4cf992e6b6a15b3e36cf.png

A
2acb2
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B
3a2b2c
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C
3c2ab2
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D
2a2cb
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Solution

The correct option is B 3a2b2c
Ref image
Given ; lS/lB=a,ySyB=c
rSrB=b
By definition, young's Modulus = Y=linearstresslinearstrain
Y=T/AΔl/l
where, T - tension in wire
A - cross sectional area of wire
Δl - change in length
l - original length
Δl=T.lY.A __(i)
FBD : Ref. image T3=mg+TB __(ii) Ref. image TB=2mg __(iii)
Put (iii) in (ii) : TS=mg+2mg=3mg
TSTB=3mg2mg=32 __(iv)
From (i) :
ΔlSΔlB=(TSlSYSAS)(TBlBYBAB)=(TSTB).(lSlB)YBABYSAS/forawire:A=πr2=32×a×1c×πr2Bπr2S/fromgivenratios
ΔlSΔlB=3a2c.b2
No correct option given

1179383_293473_ans_7132b5ae20ea4902af03c526542c8f35.png

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