A steel wire of length 20 cm and uniform cross-sectional area of `1 mm^(2)` is tied rigidly at both the ends at `45^(@)C`. If the temperature of the wire is decreased to `20^(@)C`, then the change in the tension of the wire will be
[Y for steel `= 2 xx 10^(11 Nm^(-2)`, the coefficient of linear expansion for steel `= 1.1 xx 10^(-5)//""^(@)CC^(-1)`]

Options

A. 22 N
B. 32 N
C. 55 N
D. 60 N

Answer

c

Explanation

Coefficient of linear expansion `alpha = (dL)/(L(Delta T))`
`:. (Delta L)/(L) = alpha Delta T`
and `Y = (F.L)/(A.Delta L)`
From Eq. 1 `F = YA (Delta L)/(L) = YA alpha Delta T`
`:. F = 2 xx 10^(11) xx 1 xx 10^(-6) xx 1.1 xx 10^(-5) xx 25`
`:. F = 55 N`