A table top is made of aluminium and has a hole of diameter 2 cm. An iron sphere of diameter 2.004 m is resting on this hole. Below the hole, an insulated container has 2 kg of water in it. Everything is at ambient temperature of `25^(@)C`. The table top along with the iron sphere is heated till the ball falls through the hole into the water. Find the equilibrium temperature of the ball and water system
Neglect any heat loss from ball–water system to the surrounding and assume the heat capacity of the container to be negligible.
Relevant data: Coefficient of linear expansion for aluminium and iron are `2.4 xx 10^(-5) .^(@)C^(-1)` and `1.2 xx 10^(-5) .^(@)C^(-1)` respectively. Specific heat capacity of water and iron are `4200 J .^(@)C^(-1) g^(-1)` and `450 J .^(@)C^(-1) g^(-1)` respectively. Density of iron at `25^(@)C` is `8000 kg//m^(3)`.
