Two rods of different materials and identical cross sectional area, are joined face to face at one end their free ends are fixed to the rigid walls. If the temperature of the surroundings is increased by `30^(@)C`, the magnitude of the displacement of the joint of the rod is (length of rods `l_(1) = l_(2) = 1 unit`, ratio of their young's moduli, `Y_(1)//Y_(2) = 2`, coefficients of linear expansion are `alpha_(1)` and `alpha_(2)`)

Options

A. `5(alpha_(2) - alpha_(1))`
B. `10(alpha_(1) - alpha_(2))`
C. `10(alpha_(2) - 2alpha_(1))`
D. `5(2alpha_(1) - alpha_(2))`

Answer

C

Explanation

`Y_(1) ("Strain")_(1) = Y_(2)("Strain")_(2)`
`Y_(1)[(alpha_(1)lDeltaT_(1) - x)/(l)] = Y_(2)[(alpha_(2)lDeltaT_(2) + x)/(l)]`
Displacement of the rod `x = (Y_(2)alpha_(2) - Y_(1)alpha_(1))/(Y_(1) + Y_(2)) xx l xx DeltaT`