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#5 | Potential Energy

(Physics) > Work,Energy and Power

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The potential energy of a body is given by, *U* = *A* – *Bx*^{2} (Where *x* is the displacement). The magnitude of force acting on the particle is** **

(1) Constant

(2) Proportional to *x*

(3) Proportional to *x*^{2}

(4) Inversely proportional to *x *

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The potential energy between two atoms in a molecule is given by $U\left(x\right)=\frac{a}{{x}^{12}}-\frac{b}{{x}^{6}}$; where *a* and *b* are positive constants and *x* is the distance between the atoms. The atoms are in stable equilibrium when:

(1) $x=\sqrt[6]{\frac{11a}{5b}}$

(2) $x=\sqrt[6]{\frac{a}{2b}}$

(3) *x* = 0

(4) $x=\sqrt[6]{\frac{2a}{b}}$

PMT - 1995

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A particle of mass *m* is moving in a horizontal circle of radius *r* under a centripetal force equal to –*K*/*r*^{2}, where *K* is a constant. The total energy of the particle is

** **(1) $\frac{K}{2r}$

(2) $-\frac{K}{2r}$

(3) $-\frac{K}{r}$

(4) $\frac{K}{r}$

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A particle free to move along the *x*-axis has potential energy given by $U\left(x\right)=k[1-{e}^{{(-x)}^{2}}]$ for $-\infty \le x\le +\infty $, where *k* is a positive constant of appropriate dimensions. Then

(1) At point away from the origin, the particle is in unstable equilibrium

(2) For any finite non-zero value of *x*, there is a force directed away from the origin

(3) If its total mechanical energy is *k*/2, it has its minimum kinetic energy at the origin

(4) For small displacements from *x *= 0, the motion is simple harmonic

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The potential energy of a system is represented in the first figure. the force acting on the system will be represented by

(1)

(2)

(3)

(4)

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