Two rods A and B of identical dimensions are at temperature `30^(@)C`. If A is heated upto `180^(@)C` and B `T^(@)C`, then new lengths are the same . If the ratio of the coefficients of linear expansion of A and B is 4:3,then the value of T is

Options

A. `270^(@)C`
B. `200^(@)C`
C. `230^(@)C`
D. `250^(@)C`

Answer

C

Explanation

`alpha_(A)=(DeltaL)/(L(180^(@)C-30^(@)C))`
`alpha_(B)=(DeltaL)/(L(T^(@)C-30^(@)C))`
`(alpha_(A))/(alpha_(B))=(T^(@)C-30^(@)C)/(150^(@)C)rArr4xx150^(@)C=37^(@)C-90^(@)CrArrT=230^(@)C`.