Two spheres of different material 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 radius one is 25 minutes and that for smaller sphere is 16 minutes, the ratio of thermal conductivities of material of larger sphere to smaller sphere is

Options

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

Answer

C

Explanation

`(DeltaQ)/(Deltat)=(KADeltaT)/(triangle)impliesDeltaQ=KA((DeltaT)/(Deltax))Deltat`
Assuming the thickness of the spheres to be small, we have for smaller sphere:
`("rate of heat flow")("time")=("volume of ice melted")(rho L)`
i.e., `K_1(4pir^2)(Delta theta)/(d)16=(4)/(3)pir^3rhoL` ...(i)
For larger sphere:
`K_2[4pi(2r)^2](Deltatheta)/((d)/(4))25=(4pi)/(3)(2r)^3rhoL` ...(ii)
dividing Eq. (ii) by Eq. (i)
`K_2//K_1=8//25`