The container A contains ice at `O^(@)C`. A conducting uniform rod PQ of length 4R is used to transfer heat to the ice in the container. The end P of the rod is maintained at `100^(@)C` and the other end Q is kept inside container A. The complete ice melts in 23 minutes. In another experiment, two conductors in shape of quarter circle of radii 2R and R are welded to the conductor PQ at M and N respectively and their other ends are inserted inside the container A. All conductors are made of same material and have same cross sectional area. Once again the end P is maintained at `100^(@)C` and this time the com- plete ice melts in t min- ute. Find t. Assume no heat loss from the curved surface of the rods. [Take `pi~=3.0`]

Answer

`17.5 min`