Two cylinders of equal masses, one made of material A and the other of material B, are heated to `50^(@)` C and placed on two large blocks of ice at `0^(@)` C If both the cylinders have the same height, find the ratio `(h_(A)//h_(B))` of their maximum depth of penetration in the ice. Assume that no heat is lost to the surroundings and change in gravitational potential energy is not considered `S_(A)=0.2cal g^(-1)(C^(@)),rho_(A) = 4 g cm^(-3)`
`S_(B) = 0.1 cal g^(-1) (C^(@)), rho_(B)=2 g cm^(-3)`

Answer

`4`

Explanation

`Q_(loss)=Q_(gain)`
`m_(C) S_(C) DeltaT_(C) = m_(ice) L`
`(rho_(C)Al)(S_(C))(T-0) = (rho_(ice)Ah) L`
`h=(rho_(C) lS_(C)T)/(rho_(ice)L)`
`h_(A)/h_(B)=(rho_(A)S_(A))/(rho_(B)S_(B))=((4)(0.2))/((2)(0.1))=4`