A light rod of length 200cm is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross-section 0.1 sq.cm and the other is of brass of cross-section 0.2 sq.cm . Find the position along the rod at which a weight may be hung to produce (i) equal stresses in both wires and (ii) equal strains in both wires. Ybrass=10×1011dyne/cm2 and Ysteel=20×1011dyne/cm2
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a
133.3 cm; 100 cm
b
167 cm; 50 cm
c
200 cm; 100 cm
d
None
answer is A.
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Detailed Solution
Stress same F∝A F1F2=A1A2=12⇒F2=2F1F1x=F2(2−x)F1x=2F1(2−x)⇒x=4−2x⇒x=1.333mx=133.3cmStrain same: F∝AyF1F2=A1A2y1y2=0.20.1×10×101120×1011=1F1x=F2(2−x)⇒x=2-xx=1 m=100 cm