Question

A semicircular rods is joined at its end to a straight rod of the same material and the same cross-sectional area. The straight rod forms a diameter of the other rod. The junctions are maintained at different temperatures. Find the ratio of the heat transferred through a cross section of the semicircular rod to the heat transferred through a crossection of the straight rod in a given time.
A. `2:pi`
B. `1:2`
C. `pi:2`
D. `3:2`

Answer 1

Correct Answer - A
`(dQ)/(dt)=(KaDeltatheta)/(l)`
For both rods K,A and `Deltatheta` are same.
`:. (dQ)/(dt)prop(1)/(l)`
So `((dQ//dt)_("secmicircular"))/((dQ//dt)_("straight"))=(l_("straight"))/(l_("semicircular"))=(2r)/(pi r)=(2)/(pi)`.