Q. 25

# A cube of ice of edge 4 cm is placed in an empty cylindrical glass of inner diameter 6 cm. Assume that the ice melts uniformly from each side so that it always retains its cubical shape. Remembering that ice is lighter than water, find the length of the edge of the ice cube at the instant it just leaves contact with the bottom of the glass.

Answer :

Let's assume that the edge of the ice cube just before it leaves contact with glass be “x cm” and its height of water at that time be “h cm”.

Given, inner diameter is 6 cm. Therefore, radius would be 3 cm.

Initial edge of the ice cube is 4 cm.

Let the density of water be and that of ice is

Now, the weight of the remaining ice will be balanced by the buoyant force provided from the melted water.

The mass of the ice is

Volume of water formed is

Substituting the value of h, we get

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