Two spheres of different materials one with double the radius and one-fourth wall thickness of the other are filled with ice. If the time taken for complete melting of ice in the larger sphere is `25` minutes and for smaller one is `16` minutes, the ratio of thermal conductivities of the materials of larger sphere to that of smaller sphere is:

Options

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

Answer

D

Explanation

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