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