A steel wire of length 20 cm and uniform cross-sectional `1 mm^(2)` is tied rigidly at both the ends. The temperature of the wire is altered from `40^(@)C` to `20^(@)C`. Coefficient of linear expansion of steel is `alpha = 1.1 xx 10^(-5) .^(@)C^(-1)` and Y for steel is `2.0 xx 10^(11) Nm^(2)`, the tension in the wire is

Options

A. `2.2 xx 10^(8) N`
B. 16 N
C. 8 N
D. 44N

Answer

d

Explanation

Increases in length due to rise in temperature
`Delta L = a L Delta T`
As,` Y = (FL)/(A Delta L)` so, `F = (YA Delta L)/(L) = (YA xx a L Delta T)/(L) = YA a Delta T`
`:. F = 2 xx 10^(11) xx 10^(-6) xx 1.1 xx 10^(-5) xx 20 = 44N`