A steel wire of length 20 cm and uniform cross-section 1 mm is tied rigidly at both the ends. The temperatur of the wire is altered from `40^(@)C` to `20^(@) C`. Coefficient of lienar expansion of steel is `alpha 1.1xx10^(-5)` per "C and Y for steel is `2.0xx10^(11)'Nxxm^(2)` ?, the tension in the wire is A)

Options

A. `2.2xx 10^(6) N`
B. 16 N
C. 8 N
D. 44 N

Answer

D

Explanation

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