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Q.

A steel ring of radius r and cross-sectional area A is fitted on to a wooden disc of radius R (R > r). IfYoung's modulus of the steel is Y, then the force with which the steel ring is expanded is

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a

AYr(R−r)

b

Y(R−r)r

c

AY(R−r)R

d

AY(R−r)r

answer is D.

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Detailed Solution

Change in length of ring =  2πR−2πrLongitudinal strain =2πR−2πr2πr=R−rrYoung's modulus,  Y=F/AR−rr⇒ Y=FrA(R−r)⇒F=YA(R−r)r
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