Q.

If the ratio of diameters, lengths and Young's modulus of steel and copper wires shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their lengths would be

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a

5q7sp2

b

7q5sp2

c

2q(5sp)

d

7q(5sp)

answer is B.

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Detailed Solution

As Y=FLAΔL=4FLπD2ΔL ΔL=4FLπD2Y ∴  ΔLSΔLC=FSFCLSLCDC2DS2YCYS  where subscripts S and C refer to copper and steel respectively. Here, FS=(5m+2m)g=7mg FC=5mg LSLC=q,DSDC=p,YSYC=s ∴  ΔLSΔLC=7mg5mg(q)1p21s=7q5p2s
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