The hollow 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 large radius one is 25 min and that for smaller one is 16 min , the ratio of thermal conductivities of materials of larger sphere to smaller sphere is

Options

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

Answer

B

Explanation

Thermal conductivity `K = (Q xx delta)/(A xx Delta t)`
`(K_(1))/(K_(2)) = (delta_(1))/(delta _(2)) xx((r2)/(n))^(2) xx (t_(2))/(t_(1)`
`implies (K_(1))/(K_(2)) = ((X)/(4X)) xx ((r)/(2r))^(2) xx((16)/(25))`
`implies (K_(1))/(K_(2)) = (1)/(25)`
` therefore K_(1) : K_(2) = 1 : 25`