A cube ofice 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 lighter than water, finding the length of the edge of the ice cube at the instant it just leaves contact with the bottom of the glass.

Explanation

Let edge of cube is `a` when some ice is melted.
Mass of melted ice = mass of water formed
`sigma_(ice) (4^3 - a^3"") = rho_omega[pi (3)^2 - a^2]h`
`0.9(64 - a^3)=1(9 pi - a^2)h`..(i)
`F_B + N = mg, N = 0`, when cube leaves contact
`rho_omega a^2 h = sigma_(ice) a^2 g`
`h = 0.9 a` ....(ii)
Form (i) and (ii)
`0.9 (64 - a^3)=(9pi - a^2)(0.9 a)`
`64 -a^3 = 9 pi a - a^3`
`a = (64)/(9 pi) cm`
=`2.26 cm`.