Two rods of same length & material transfer a given amount of heat in 12 s when they are joined end to end. But when they are joined length wise parallel to each other they will transfer same amount of heat in same condition in time

• A

  24 s
• Correct answer
  B

  3 s
• C

  1.5 s
• D

  48 s

Solution

Let the heat transferred be Q
When rods are joined end to end, heat transferred by each rod $=\mathrm{Q}=\frac{\mathrm{KA} \Delta \theta}{2 l} \times 12...(i)$
When rods are joined lengthwise, $\mathrm{Q}=\frac{\mathrm{K} 2 \mathrm{~A} \Delta \theta}{l} \mathrm{t}...(ii)$
From equation (i) and (ii), $\begin{aligned} & \frac{\mathrm{K} 2 \mathrm{~A} \Delta \theta}{l} \mathrm{t}=\frac{\mathrm{KA} \Delta \theta}{2 l} \times 12 \\ \therefore \quad & \mathrm{t}=\frac{12}{2 \times 2}=3 \mathrm{~s} \end{aligned}$

Hence, the correct answer is option: 'B'.