Two rods of different materials having coefficient of thermal expansion `alpha_(1), alpha_(2)` and young's moduli `Y_(1) ,Y_(2)` respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If `alpha_(1) :alpha_(2)=2 : 3`, the thermal stresses developed in the two rods are equal provided `Y_(1) : Y_(2)` is equal to

Options

A. ` 2 : 3`
B. `1 : 1`
C. `3 : 2`
D. `4 : 9`

Answer

C

Explanation

Strain `=(Deltal)/l=(lalphaDeltatheta)/l=alpha Delta theta`
Stress `=Yxx "Starin" =Yalpha Delta theta`
`" " ("Stress")_(1)=(Stress)_(2)`
`therefore" " Y_(1) alpha_(1)=Y_(2)alpha_(2)`
or `" " (Y_(1))/(Y_(2))=(alpha_(2))/(alpha_(1))=3/2`