Two uniform brass rods A and B of lengths l and 2l and radii 2r and r respectively are heated to the same temperature. The ratio of the increase in the length of A to that of B is :

Options

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

Answer

C

Explanation

`V_1 = l xx 2 pi (2r)^(2)`
`V_2 = 2l xx 2 pi (r)^(2)`
`Delta V_1 = V_1 gamma Delta T and Delta V_2 = V_2 gamma Delta T`
`(Delta V_1)/(Delta V_2) = (I (2r)^2)/(2lr^2) = (2)/(1)`.