A student wants to arrange 4 identical spheres(of radius R) on a two dimensional floor as close as possible.Finally he could arrange them.Identify the type and dimensions of the figure obtained by joining their centers. Could he occupy the whole available space, if not, then what type of voids were generated.Calculate their number and radius of small ball that can be fitted in them.
Text Solution
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No, Rhombous: 2R, 60º, 120º ; Triangular voids; 2 voids, 0.155 R.
Sol. 
Rhombous. 60 o and 120 o Whole available space not occupy.
No. of void = 2
Type of void = Triangular
Sin 60 = 
= 
⇒ r = 0.155 R
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