Question

The velocity \((v)\) of a particle \((\) under a force \(F)\) depends on its distance \((x)\) from the origin \((\) with \(x>0) v \propto \frac{1}{\sqrt{x}} .\) Find how the magnitude of the force \((F)\) on the particle depends on \(x\)
(A) \(F \propto \frac{1}{x^{\frac{3}{2}}}\)
(B) \(F \propto \frac{1}{x}\)
(C) \(F \propto \frac{1}{x^{2}}\)
(D) \(F \propto x\)

Answer 1

Ans: (C)
Hint \(: v \propto \frac{1}{\sqrt{x}} \therefore v=\frac{K}{\sqrt{x}}\)
$$
F \propto \frac{v d v}{d x}=\frac{K}{\sqrt{x}} \times \frac{-K}{2} x^{-3 / 2}=\frac{-K^{2}}{2 x^{2}}, F \propto \frac{1}{x^{2}}
$$

Answer 2

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Answer 3

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