A wire elongates by 1.0 mm when a load W is hung from it. If this wire goes over a a pulley and two weights W each are hung at the two ends, he elongation of he wire will be

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ext{ Let the Young's modulus of the material of the wire be Y } . 	ext{ Force = Weight = W (given) } 	ext{ Let C . S . A . = A} 	ext{ x = 1 mm = Elongation in the first case } 	ext{ Length = L } Y = W/A/x/L = WL/Ax 	ext{Let y be the elongation on one side of the wire when put in a pulley }. 	ext{ When put in a pulley, the length of the wire on each side }= L/2 \frac{W/A}{y/L/2} = Y \Rightarrow \frac{W/A}{y/L/2} = \frac{WL}{	ext{ Ax }} \Rightarrow y = x/2 	ext{ Total elongation in the wire = 2y }= 2\left( x/2 ight) = x = 1	ext{ mm}

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