Two identical conducting rods are first connected independently to two vessels, one containing water at `100^@C` and the other containing ice at `0^@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 `q_1/q_2` is
(a) `1/2` (b)`2/1` (c)`4/1` (d)`1/4`

Options

A. `1/2`
B. `2/1`
C. `4/1`
D. `1/4`

Answer

C

Explanation

Initially the rods are in parallel
`Q/t = (theta_(1)-theta_(2))/R`
`rArr (Q/t)_(1) = (mL)/t = q_(1)L = (100-0)/(R/2)`............(i)
Finally when rods are in series
`rArr (Q/t)_(2) = (mL)/t = q_(2)L = (100-0)/(2R)`..............(ii)
From Eqs. (i) and (ii),
`q_(1)/q_(2) = 4/1`