A wire, 3 m in length and 1 mm in diameter at 30 ° C is kept in low temperature at - 170 ° C and is stretched by hanging a weight of 10 kg at one end. The change in length of the wire is [ Y = 2 × 10 11 N m - 2 , g = 10 ms - 2 and α = 1.2 × 10 - 5 / ° C ]

Step-by-step solution

The change in length of the wire due to change in temperature = α L T = 1.2 × 10 - 5 × 3 × - 170 - 30 = - 7.2 × 10 - 3 m The change in the length of the wire due to the stretching force = F   L A   Y =   10 × 10 × 3 0 .75 × 10 - 6 × 2 × 10 11 = 2 × 10 - 3   m The total change in the length of the wire = - 7.2 × 10 - 3 + 2 × 10 - 3 = - 5.2 × 10 - 3   m = - 5 . 2   mm The negative sign indicates contraction of the wire