NEET-XII-Physics
14: Some Mechanical Properties of Matter
- #28Consider an ice cube of edge 1.0 cm kept in a gravity-free hall. Find the surface area of the water when the ice melts. Neglect the difference in densities of ice and water.Ans : Given:
Edge of the ice cube
(a) = 1.0 cm
The water that is formed due to the melting of ice acquires a spherical surface.
In the absence of gravity, let the radius of the spherical surface be r.
Volume of ice cube = volume of spherical surface of water
`` \Rightarrow {a}^{3}=\frac{4}{3}\,\mathrm{\,\pi \,}{r}^{3}``
`` \Rightarrow r={\left[\frac{3{\,\mathrm{\,a\,}}^{3}}{4\,\mathrm{\,\pi \,}}\right]}^{1/3}``
Surface area of spherical water surface = 4Ï€r2
`` =4\,\mathrm{\,\pi \,}{\left[\frac{3{a}^{3}}{4\,\mathrm{\,\pi \,}}\right]}^{2/3}``
`` ={\left(36\,\mathrm{\,\pi \,}\right)}^{1/3}{\,\mathrm{\,cm\,}}^{2}``
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