Three conducting rods of same material and cross-section are show… - Vidyadip

MCQ

Three conducting rods of same material and cross-section are shown in figure. Temperatures of$ A, D$ and $C$ are maintained at $20^o C, 90^o C$ and $0^o C$. The ratio of lengths of $BD$ and $BC$ if there is no heat flow in $AB$ is:

A
$2 / 7$
✓
$7 / 2$
C
$9 / 2$
D
$2 / 9$

✓

Answer

Correct option: B.

$7 / 2$

b
since there is no flow of heat in rod, so temperature of $B$ is equal to temperature at $A$

i.e.,

$\theta_{B}=\theta_{A}=20^{\circ} C$

Heat flowing through $D B$ per second $=$ heat flowing through

i.e., $\frac{K A\left(90^{\circ}-20^{\circ}\right)}{I_{B D}}=\frac{K A\left(20^{\circ}-0^{\circ}\right)}{I_{B C}}$

$\therefore \frac{I_{B C}}{I_{B D}}=\frac{2}{7}$

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