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 q1and q2 g / s be the rate of melting of ice in two cases respectively. The ratio of $\frac{q1}{q2}$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Initially the rods are place on vessels as shown below

$\frac{Q}{t}=\frac{({\theta }_1-{\theta }_2)}{R}\Rightarrow {\left(\frac{Q}{t}\right)}_l=\frac{mL}{t}=q_{1}L=\frac{(100-0)}{\frac{R}{2}}$ ...... (i)

Finally when rod are joined end to end as shown

$\Rightarrow {\left(\frac{Q}{t}\right)}_2=\frac{mL}{t}=q_{2}L=\frac{(100-0)}{2R}$ .........(ii)

From equation (i) and (ii) , $\frac{q_1}{q_2}=\frac{4}{1}$