A particle is acted by a force , where is a +ve constant. Its potential energy at is zero. Which curve correctly represents the variation of potential energy of the block with respect to [2004]

Question

A particle is acted by a force $F = k x$ , where $k$ is a +ve constant. Its potential energy at $x = 0$ is zero. Which curve correctly represents the variation of potential energy of the block with respect to $x$ [2004]

Smart Achievers · Accepted Answer

(2)

$For conservative forces Δ U = - W$

$Δ U = - \int_{0}^{x} F d x or Δ U = - \int_{0}^{x} k x d x$

$\Rightarrow U_{(x)} - U_{(0)} = - \frac{k x^{2}}{2} (∵ U_{(0)} = 0)$

$∴$ $U_{(x)} = - \frac{k x^{2}}{2} \Rightarrow x^{2} = \frac{- 2 U_{x}}{k}$

It represents a parabola below the $x$ -axis symmetrical.

Solution

Q.
A particle is acted by a force $F = k x$ , where $k$ is a +ve constant. Its potential energy at $x = 0$ is zero. Which curve correctly represents the variation of potential energy of the block with respect to $x$ [2004]

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Solution

Q. A particle is acted by a force F=kx, where k is a +ve constant. Its potential energy at x=0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x [2004]

1

2

3

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Ans. (2) For conservative forces ΔU=-W ΔU=-∫0xF dx or ΔU=-∫0xkx dx ⇒U(x)-U(0)=-kx22 (∵ U(0)=0) ∴ U(x)=-kx22 ⇒ x2=-2Uxk It represents a parabola below the x-axis symmetrical.

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Q.
A particle is acted by a force $F = k x$ , where $k$ is a +ve constant. Its potential energy at $x = 0$ is zero. Which curve correctly represents the variation of potential energy of the block with respect to $x$ [2004]