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A truck is pulling a car out of a ditch by means of a steel cable 9.1 m long and radius 5 mm. When the car just begins to move, the tension in the cable is 800 N. If Y of cable is 200 GPa, the stretching in the cable is

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0.5 mm

1 mm

2 mm

4 mm

answer is A.

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Detailed Solution

$Y = \frac{F l}{Ae} \Rightarrow e = \frac{F l}{AY}$

$e = \frac{800 x 9.1}{3.14 {(5 x 10^{- 3})}^{2} x 2 x 10^{11}} = \frac{800 x 9.1}{3.14 x 25 x 2 x 10^{- 6} x 10^{11}}$
e = 46.4 x 10^–5 m; e = 0.464 mm; e = 0.5 mm

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