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Q.

Two wires of same length and same material but of radii r and 2r are stretched by forces F and f respectively to produce equal elongation. The ratio F to f is

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a

1 : 1

b

1 : 2

c

2 : 1

d

1 : 4

answer is D.

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Detailed Solution

Given, r1=r,r2=2rNow, we know that,  Y=FA⋅lΔl=Fπr2⋅lΔlSo,  Fπr12=fπr22    (∵l,Δl and Y are same )⇒ Ff=r12r22⇒Ff=r24r2⇒Ff=14
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Two wires of same length and same material but of radii r and 2r are stretched by forces F and f respectively to produce equal elongation. The ratio F to f is