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An ice ball of radius a and mass m is pl...

An ice ball of radius a and mass m is placed at `0^@C` inside a thick hollow sphere of inner and outer radii a and b whose thermal conductivity varies as `k=alpha/r^2`, where `alpha` is a positive constant and r is the distance from centre. The temperature of surrounding is `theta_0` and latent heat of fusion for ice is `L_f`. Then , time required to completely melt the ice ball is (Neglect the contraction in volume when ice melts into water and any change in thermal resistance due to melting of ice of the system.)

A

`(mL_f ln (b/a))/(4pialpha theta_0)`

B

`(mL_f (b-a))/(2pialphatheta_0)`

C

`(mL_f(b-a))/(pialphatheta_0)`

D

`(mL_f(b-a))/(4pialphatheta_0)`

Text Solution

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The correct Answer is:
D
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