Solid State - Result Question 41
####41. (i) Marbles of diameter $10 mm$ are to be put in a square area of side $40 mm$ so that their centres are within this area.
(ii) Find the maximum number of marbles per unit area and deduce an expression for calculating it.
$(2003,4 M)$
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Solution:
- (i) Side of square $=40 mm$ Diameter of marble $=10 mm$ Number of marble spheres along an edge of square with their
centres within the square $=5$ (shown in diagram) Maximum number of marbles per unit area $=5 \times 5=25$
(ii) If $x mm$ is the side of square and $d$ is diameter of marble then maximum number of marbles on square area with centres within square area can be known by the following general formula :
$$ N=\left(\frac{x}{d}+1\right)^{2} $$
