One end of a `2.35m` long and `2.0cm` radius aluminium rod `(K=235W.m^(-1)K^(-1))` is held at `20^(@)C`. The other end of the rod is in contact with a block of ice at its melting point. The rate in `kg.s^(-1)` at which ice melts is [Take latent heat of fusion for ice as `(10)/(3)xx10^(5)J.kg^(-1)`]

Options

A. `48pixx10^(-6)`
B. `24pixx10^(-6)`
C. `2.4pixx10^(-6)`
D. `4.8pixx10^(-6)`

Explanation

`l=2.35m`, `r=2cm`
`K=235`, `T=20^(@)C`, `DeltaT=20^(@)C`
`(dH)/(dt)=((dm)/(dt))L_(f)`
`((dm)/(dt))=((dH)/(dt))_(L_(f))^(bot)=(KA)/(l)(DeltaT)(1)/(L_(f))`
`((dm)/(dt))=(235xxpi(2xx10^(-2))^(2)xx20)/(2.35xx(10)/(3)xx105)`
`=(100pixx4xx10^(-4)xx20)/(10xx105)xx3`
`=2.4pixx10^(-6)ks//sec`