The Thin walled spheres of different matrials one with double the radius and one fourth wall thickness of the other are filled with ice if the time taken for complete metting of ice in the sphere of larger radius is `25 min` and that for smaller one is `6min` the ratio of the thermal condutivities of the matrials of larger sphere to the smaller sphere is .

Options

A. `4:5`
B. `25:1`
C. `1:25`
D. `8:25`

Answer

D

Explanation

`int dR = int (dr)/(4pir^(2)K) = (1)/(4piK) [(r_(2)-r_(1))/(r_(2)r_(1))]`
`[R = "thermal resistance"]`
`Q = (4pi K Deltatheta)/(((r_(2)-r_(1))/(r_(1)r_(2))))=(4piKDeltatheta)/(((t)/(r^(2))))`
`(mL)/(time)=(4piKDeltatheta)/(((t)/(r^(2))))[m=rhoxx(4)/(3)pir^(3)]`
`(rhoL)/(time)((K)/(tr))xx"constant"`
`(25)/(16) = ((t)/(4)2rK_(s))/(trK_(L))=(1)/(2)(K_(s))/(K_(L)),(K_(L))/(K_(s))=(8)/(25)` .