Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The point A and B are maintained at different temperature. Find the ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross section of the straight rod in a given time.

Options

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

Answer

A

Explanation

(1) `R_("circular") = R_(1) prop pi r`
`R_("straight") = R_(2) prop 2r`
`theta_(A) - theta_(B) = i_(1) R_(1) = i_(2) R_(2)`
`(i_(1))/(i_(2)) = (R_(2))/(R_(1)) = (2r )/(pi r) = (2)/(pi)`