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)/(4pir^(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=rhoxx4/3pir^(3)]`
`(rhoL)/time =(K/(tr))xxconstant`
`time propto(tr)/K`
`25/16=(t/4(2rK_(s))/(trk_(L))=(1k_(s))/(2k_(l))`
`(k_(L))/(k_(s))=8/25`