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$_2$ gram per second be the rate of melting of ice in the two cases respectively. The ratio $\frac{q_1}{q_2}$ is

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

Answer 1

Answer: (C)

$\frac{4}{1}$

Answer 2

$\frac{dQ}{dt}=L\bigg(\frac{dm}{dt}\bigg)$
or $\, \, \, \frac{Temperature \, difference}{Thermal \, resistance} =L\bigg(\frac{dm}{dt}\bigg)$
or $\frac{dm}{dt} \propto \frac{1}{Thermal \, resistance} \Rightarrow q$
In the first case rods are in parallel and thermal resistance is
$\frac{R}{2}$ while in second case rods are in series and thermal
resistance is 2R.
$\frac{q_1}{q_2}=\frac{2R}{R / 2 }=\frac{4}{1}$
Hence, the correct option is (c)