A steel wire,3.2 m long,has a diameter of 1.2 mm.The wire stretches 1.6 mm when it bears a load.Young's modulus for steel is 2.0 × 10¹¹ Pa.The mass of the load is closest to A)12 kg. B)16 kg. C)20 kg. D)24 kg. E)28 kg.

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The correct answer is A.The stress on the wire is:$$\sigma = \frac{F}{A} = \frac{4F}{\pi d^2}$$where F is the load, A is the cross-sectional area of the wire, and d is the diameter of the wire.The strain on the wire is:$$\epsilon = \frac{\Delta L}{L} = \frac{1.6 	ext{ mm}}{3.2 	ext{ m}} = 5.0 	imes 10^{-4}$$Young's modulus is:$$Y = \frac{\sigma}{\epsilon} = \frac{4F}{\pi d^2 \epsilon}$$Substituting the given values into the equation, we get:$$2.0 	imes 10^{11} 	ext{ Pa} = \frac{4F}{\pi (1.2 	imes 10^{-3} 	ext{ m})^2 (5.0 	imes 10^{-4})}$$Solving for F, we get:$$F = 12 	ext{ kg}$$

A Steel Wire,3