Correct Answer - 5

For any general moment `1000^(@)C`.

`i_(H) = (1000 -T)/(R_(eq)) = (dQ)/(dt)`

where `R_(eq) = int (dx)/(k(4pix^(2))) = (1)/(4pik) ((x^(-2+1))/(-2+1))_(R_(1))^(R_(2))`

`R_(eq) = (1)/(4pik) {(1)/(R_(1))-(1)/(R_(2))} = (1)/(50)`

Now, mass of water inside cavity

`M = rho xx (4)/(3) pi R_(1)^(3)`

`(dQ)/(dt) = MS (d theta)/(dt) = (1000 -T)/(R_(eq)) (d theta =dT)`

`overset(100^(@))underset(0^(@))int (dT)/((1000-T)) = (1)/((R_(eq)MS)) overset(t)underset(0)int dt`

`t = R_(eq) MS xx {ln((1000)/(900))}`