Q.If \(a \propto \frac{1}{b^2}\), then the correct statement is: (a) \(b \propto \sqrt a\) (b) \(b \propto \cfrac {1}{\sqrt a}\) (c) \(b \propto \cfrac {1}{-\sqrt a}\) (d) \(b \propto \cfrac {1}{\pm \sqrt a}\)
Answer: D
\(a \propto \frac{1}{b^2}\) i.e., \(a = k \cdot \frac{1}{b^2}\) [where \(k\) is a non-zero constant] i.e., \(ab^2 = k\) i.e., \(b^2 = \frac{k}{a}\) i.e., \(b = \pm \sqrt{\frac{k}{a}}\) i.e., \(b \propto \pm \frac{1}{\sqrt{a}}\) [since \(k\) is a non-zero constant]
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