Three rods AB, BC and BD of same length l and cross section A are arranged as shown. The end D is immersed in ice whose mass is 440 g and is at `0^@C`. The end C is maintained at `100^@C`. Heat is supplied at constant rate of 200 cal/s. Thermal conductivities of AB, BC and BD are K, 2K and `K//2`, respectively Time after which whole ice will melt is (`K=100 cal//m-s^@C A=10cm^2,l=1cm`)

Options

A. 400 s
B. 600 s
C. 700 s
D. 800 s

Answer

D

Explanation

Let `theta` be the temperate of B
`(2KA(theta-100))/(l)+(((K)/(2))A(theta-0))/(l)=200`
Substituting values `theta=880^@C`
Also from `BrarrD,((K)/(2)A(theta-0))/(l)=(440)/(5) xx 80`
`t=800s`