A force F acting on a body depens on its displacement x as F ∝ x n . The power delivered by F will be independent of x if n is-

v d x d v = k x n gives v ∝ x 2 n + 1 P = F v ∝ x 2 3 n + 1 ; for P independent of x: 3 n + 1 = 0 , so n = − 3 1 Answer (B)

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PhysicsW.E.P.316Medium2 minQB

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A force F acting on a body depens on its displacement x as $F \propto x^{n}$ . The power delivered by F will be independent of x if n is-

Answer:

Solution:

$v \frac{d v}{d x} = k x^{n}$ gives $v \propto x^{\frac{n + 1}{2}}$

$P = F v \propto x^{\frac{3 n + 1}{2}}$ ; for P independent of x: $3 n + 1 = 0$ , so $n = - \frac{1}{3}$

Answer (B)

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:316

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