A stainless-steel orthodontic wire is applied to a tooth, as in the figure below

Question

A stainless-steel orthodontic wire is applied to a tooth, as in the figure below. The wire has an unstretched length of 2.50 cm and a radius of 0.14 mm. If the wire is stretched 0.11 mm, find the magnitude and direction of the force on the tooth. Disregard the width of the tooth and assume Young's modulus for stainless steel is 1.8 x1011 Pa.
magnitude ______________N

So -> L= 0.025m, R= 0.0014m, L=0.0011m

and -> F =Y(r2)(L/Lo)

so -> F = 1.8x1011 x x (0.0014)2 x 0.0011  / 0.025 = 48767

The Other way I found was 1.8x1011 x x (0.0014)2 x 0.025  / 0.0011

The answer should be 48.8N

How do I get here? What am I missing?

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Explanation / Answer

you did wrong in the conversion R = 0.14 mm = 0.14 x 10^-3 m = 0.00014 m and L = 0.00011 m

L= 0.025m, R= 0.00014m, L=0.00011m

and -> F =Y(r2)(L/Lo)

so -> F = 1.8x1011 x x (0.00014)2 x 0.00011  / 0.025 = 48.8 N

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