A wire of radius \(1 mm\) is bent in the form of a circle of radius \(10 cm\). The bending moment will be \((Y =2\times10^{11}N/m^{2})\)

(A) 3.14 N/m

(B) 6.28 N/m

(C) 1.57 N/m

(D) 15.7 N/m

(A) 3.14 N/m

(B) 6.28 N/m

(C) 1.57 N/m

(D) 15.7 N/m

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A wire of radius \(1 mm\) is bent in the form of a circle of radius \(10 cm\). The bending moment will be \((Y =2\times10^{11}N/m^{2})\)

(A) 3.14 N/m

(B) 6.28 N/m

(C) 1.57 N/m

(D) 15.7 N/m

(A) 3.14 N/m

(B) 6.28 N/m

(C) 1.57 N/m

(D) 15.7 N/m

Answer: C

Bending Moment \(C=\dfrac { Y{ I }_{ G } }{ R } \)

where \(Y= 2\times { 10 }^{ 11 }N/{m}^{2}\)

\(R= 10cm= 0.1m\)

\({ I }_{ G }=\dfrac{\pi{R}^{4}}{4} = \dfrac{\pi{0.1}^{4}}{4} =7.85\times{10}^{-5} m^{4}\)

Put these in the expression for \(C\),

\(C=1.57N/m\)

Bending Moment \(C=\dfrac { Y{ I }_{ G } }{ R } \)

where \(Y= 2\times { 10 }^{ 11 }N/{m}^{2}\)

\(R= 10cm= 0.1m\)

\({ I }_{ G }=\dfrac{\pi{R}^{4}}{4} = \dfrac{\pi{0.1}^{4}}{4} =7.85\times{10}^{-5} m^{4}\)

Put these in the expression for \(C\),

\(C=1.57N/m\)

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