Two rods of equal cross sections area are joined end the end as shown in figure. These are supported between two rigid vertical walls. Initially the rods are unstrained .

If temperature of system is increased by `DeltaT` then shifting in junction if junction if `Y_(1)alpha_(1) gt Y_(2)alpha_(2)` is given by -

Options

A. `(l_(1)l_(2)(Y_(1)alpha_(2) - Y_(2)alpha_(1)))/(Y_(1)l_(1) + Y_(2)l_(2))`
B. `(l_(1)l_(2)(Y_(1)alpha_(1) - Y_(2)alpha_(2)))/(Y_(1)l_(2) + Y_(2)l_(1))`
C. `(l_(1)l_(2)(Y_(1)alpha_(1) - Y_(2)alpha_(2)))/(Y_(1)l_(1) + Y_(2)l_(2))`
D. None of these

Answer

B

Explanation

Let shifting in Junction be x towards right then `((Deltal)/(l))_(1) = (l_(1)alpha_(1)DeltaT-x)/(l_(1)) , ((Deltal)/(l))_(2) = (l_(2)alpha_(2)DeltaT + x)/(l_(2))` But `Y_(1) ((Deltal)/(l))_(1) = Y_(2)((Deltal)/(l))_(2)`
So x = `(l_(1)l_(2)(Y_(1)alpha_(1) - Y_(2)alpha_(2))DeltaT)/(Y_(1)l_(2) + Y_(2)l_(1))`