Two identical rods are connected between two containers. One of them is at `100^(@)C` containing water and another is at `0^(@)C` containing ice. If rods are connected in parallel then the rate of melting of ice is `q_(1)g//s` . If they are connected in series then teh rate is `q_(2)g//s` . The ratio `q_(2)//q_(1)` is

Options

A. `1//8`
B. `1//4`
C. `1//2`
D. `4`

Answer

B

Explanation

The resultant conductivity of combination of two rods ,
in parallel is, `K_(p) =K_(1) + K_(2) =K + K=2 K`
in secries is, `K_(s) =(K_(1)K_(2))/(K_(1) + K_(2)) = (KxxK)/(K+K) = (K)/(2)`
`q_(1) =((2K) A(100-0))/(x) = (2KAxx100)/(x)`
`q_(2) =((K)/(2)) (A(100-0))/(x) = (KAxx100)/(2x)`
`:. (q_(2))/(q_(1)) = (KAxx100)/(2x)xx(x)/(2KAxx100) =(1)/(4)`