Two spheres of different materials, one with double the radius but `1//4` th wall thickness than other are filled with ice. If the time taken for complete melting of ice in the bigger sohere is 25 minutes and that in smaller is 16 minutes, the ratio of the thermal conductivities of larger to the smaller is :

Options

A. `5//4`
B. `3//4`
C. `8//25`
D. `2//5`.

Answer

C

Explanation

Volume of bigger sphere is 8 times the smaller sphere.
`:.` Amount of ice in bigger sphere is 8 times the ice is smaller sphere.
`:.8Q=(k_(1)4pi(2r)^(2)(T_(1)-T_(2))xx25)/(l//4)`
`Q=(k_(2)4pir^(2)(T_(1)-T_(2))xx16)/(l)`
`:.(8Q)/(Q)=(k_(1))/(k_(2))*4xx(25)/(16)xx4`
`8=(25k_(1))/(k_(2))" "rArr" "(k_(1))/(k_(2))=(8)/(25)`
Thus correct choice is (c ).