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Question

The weight of a metallic solid sphere varies as the density of its material when its diameter is constant and varies as the diameter when density is constant. A sphere having density 2.1gm/cm3 and diameter 2 cm, weighs 2.2 gm. Find the weight of a sphere whose diameter is 1 cm and density is 6.3 gm/cm3.

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Solution

Let W, D and d denote the weight, density and diameter of the metallic solid sphere, respectively.Given:W α D ...(i) d is a constant.W α d ...(ii) D is a constant.From (i) & (ii), we get:W α Dd W=kDd k is a constant.We have:W=2.2 gm when D= 2.1 gm/cm3 and d=2 cm.2.2=k×2.1×2 k=2.22.1×2 k=0.52When d=1 cm and D=6.3 gm/cm3, we get:W=0.52×6.3×1 =3.27 gm3.3 gm

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