Heat Transfer

To solve the problem of finding the ratio of the specific heat of the metal to that of water, we need to apply the principle of conservation of energy. When the metal ball is dropped into the water, heat lost by water = heat gained by the metal. Let and be the mass and specific heat of the metal, and and be the mass and specific heat of water, respectively. Given:

Applying the principle of conservation of energy:

Substituting the known values:

Simplifying the equation gives:

Rearranging for the ratio of specific heat:

Therefore, the ratio of specific heat of the metal to that of water is .

Step 1: Heat gained and lost calculation
The heat lost by water at to reach is: The heat gained by ice at to reach is: The heat required to melt the ice at is: The heat gained by melted ice water at to reach is: Step 2: Applying heat balance equation
Since no heat is lost to the surroundings, we equate heat lost by water to the heat gained by ice: Solving for : Thus, the correct answer is option (B) 20 g.