Three rods made of same material and having the same cross-section have been joined as shown. In the figure.Each rod is of the same length. The left and right ends are kept at `0^@C and 90^@C` respectively. The temperature of the junction of the three rods will be

Options

A. `45^@C`
B. `60^@C`
C. `30^@C`
D. `20^@C`

Answer

B

Explanation

(b) Let `theta^@C` be the temperature at B. Let Q id the heat
flowing per second from A to B on account of
temeperature difference.
`:. Q=(KA(90- theta))/l…..(i)`

By symmetery, the same will be the case hor heat flow
from C to B.
`:. The heat flowing per second from B to D will be
`2Q=(KA( theta-0))/l.......(ii)`
Dividing ea.(ii) by eq. (i)
`2= theta/(90- theta) rArr theta=60^@`