Two conductors of the same material have their diameters in the ratio 1 : 2 and their lengths in the ratio 2:1. If the temperature difference between their ends is the same, then the ratio of amounts of heat conducted per second through them will be

Options

A. `4:1`
B. `1:4`
C. `8:1`
D. `1:8`

Answer

D

Explanation

Thermal potentials `T_(1)` and `T_(2)` are the same. Heat flowing per second will depend on the thermal resistance. `R_(1)=(p.l)/(A)=(p.2l)/(pir^(2))` where `p=(1)/(k)`    (k is the thermal conductivity)
`R_(2)=(p.l)/(pi.4r^(2))`
`therefore`   `R_(1)` will conduct less heat. Heat flowing per second is equivalent to current The ratio of heat conducted `prop(R_(2))/(R_(1))` 
=`(pl)/(pi.4r^(2)).(pir^(2))/(p.2l)=(1)/(8)`