Two metal rods A and B are having their initial lengths in the ratio `2:3`, and coefficients of linear expansion in the ratio `3:4`. When they are heated through same temperature difference the ratio of their linear expansions is …………….. .

Options

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

Answer

a

Explanation

`Deltal_(A)=l_(A)alpha_(A)Deltat, Deltal_(B)=l_(B)alpha_(B)Deltat`
`(Deltal_(A))/(Deltal_(B))=(l_(A)alpha_(A))/(l_(B)alpha_(B))=(2)/(3)xx()/(4)=(1)/(2)rArr Deltal_(A):Deltal_(B)=1:2`