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. `5:4`
C. `25:8`
D. `8:25`

Answer

4

Explanation

`H=Q/t=(KA)/(l)(theta_(1)-theta_(2))`
`=(mL)/(t)=(K4piR^(2))/(l)(theta_(1)-theta_(2))`
`(VrhoL)/(t)=(K4piR^(2))/(l)(theta_(1)-theta_(2))`
`(4)/(3)(pir^(3)rhoL)/(t)=(K4pir^(2))/(l) (theta_(1)-theta_(2))K propto (rl)/(t)`
`(K_(1))/(K_(2))=(r_(1))/(r_(2)).(l_(1))/(l_(2))xx(t_(2))/(t_(1))`
`(K_(1))/(K_(2))=(2r)/(r).(l)/(4l).(16)/(25)=(8)/(25)`