Question

Two identical conducting rods are first connected independently to two vessels, one containing water at $100^{\circ} C$ and the other containing ice at $0^{\circ} C$. In the second case, the rods are joined end to end and connected to the same vessels. Let $q_{1}$ and $q_{2} g / s$ be the rate of melting of ice in two cases, respectively. The ratio of $q_{1} / q_{2}$ is

• A. $\frac{1}{2}$
• B. $\frac{2}{1}$
• C. $\frac{4}{1}$
• D. $\frac{1}{4}$

Answer 1

Answer: (C)

Initially the rods are placed in vessels as shown below.


$\frac{Q}{t}=\frac{\left(\theta_{1}-\theta_{2}\right)}{R}$
$ \Rightarrow\left(\frac{Q}{t}\right)_{1}=\frac{m L}{t}$
$=q_{1} L=\frac{(100-0)}{\frac{R}{2}} $... (i)
Finally when rods are joined end to end as shown,

$\Rightarrow\left(\frac{Q}{t}\right)_{2}=\frac{m L}{t}$
$=q_{2} L=\frac{(100-0)}{2 R}$ ....(ii)
From equations (i) and (ii), $\frac{q_{1}}{q_{2}}=\frac{4}{1}$