A steel rail of length 5 m and area of cross section `40 cm^2` is prevented from expanding along its length while the temperature rises by `10^@C` . If coefficient of linear expansion and Young's modulus of steel are `1.2 xx 10^5K^1` and `2 xx 10^11 Nm^2` respectively, the force developed in the rail is approximately:

Options

A. `2 xx 10^7 N`
B. `1 xx 10^5 N`
C. `2 xx 10^9 N`
D. `3 xx 10^(-5) N`

Answer

B

Explanation

`F = AY alpha Delta T = 40 xx 10^(-2) xx 2 xx 10^11 xx 1.2 xx 10^5 xx 10 = 0.96 xx 10^5 ~~ 1 xx 10^5 N`