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)/(pi)`
C. `pi`
D. `(pi)/(2)`

Answer

A

Explanation

`(dQ)/(dt) = (KA Delta theta)/(l) `, for both rods `K, A` and `Delta theta` are same
`rArr (dQ)/(dt) prop 1/l ` so `((dQ//dt)_("semicircular"))/((dQ//dt)_("straight"))`
`=(l_("straight"))/(l_("semicircular")) = (2r)/(pi r) = 2/(pi)`.