The potential energy $$\mathrm{U}$$ of a system is given by $\mathrm{U}=$ $\mathrm{A}$ $-$ ${\mathrm{Bx}}^{2}$ (where $$\mathrm{x}$$ is the position of its particle and $$\mathrm{A},$$ $$\mathrm{B}$$ are constants). The magnitude of the force acting on the particle is:
1. constant

2. proportional to $$\mathrm{x}$$

3. proportional to ${\mathrm{x}}^{2}$

4. proportional to $\left(\frac{1}{\mathrm{x}}\right)$

Subtopic:  Potential Energy: Relation with Force |
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The potential energy of a particle varies with distance r as shown in the graph. The force acting on the particle is equal to zero at:

 1 P 2 S 3 Both Q and R 4 Both P and S
Subtopic:  Potential Energy: Relation with Force |
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A particle is moving such that the potential energy U varies with position in metre as U (x) = ($4{\mathrm{x}}^{2}$ - 2x + 50) J. The particle will be in equilibrium at:
1. x = 25 cm
2. x = 2.5 cm
3. x = 25 m
4. x = 2.5 m

Subtopic:  Potential Energy: Relation with Force |
78%
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The potential energy of a particle in a force field is $$U=$$$\frac{A}{{r}^{2}}-\frac{B}{r}$ where $$A$$ and $$B$$ are positive constants and $$r$$ is the distance of the particle from the center of the field. For stable equilibrium, the distance of the particle is:

 1 $$\frac{B}{A}$$ 2 $$\frac{B}{2A}$$ 3 $$\frac{2A}{B}$$ 4 $$\frac{A}{B}$$

Subtopic:  Potential Energy: Relation with Force |
77%
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AIPMT - 2012
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The figure shows the potential energy function U(x) for a system in which a particle is in a one-dimensional motion. What is the direction of the force when the particle is in region AB? (symbols have their usual meanings)

1.  The positive direction of x

2.  The negative direction of X

3.  Force is zero, so direction not defined

4.  The negative direction of y

Subtopic:  Potential Energy: Relation with Force |
64%
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The potential energy of a particle of mass 1 kg free to move along the X-axis is given by $$U(x) = (3x^2-4x+6)~\text{J}$$. The force acting on the particle at x = 0 will be:

1.  2$\stackrel{^}{\mathrm{i}}$ N

2.  -4$\stackrel{^}{\mathrm{i}}$ N

3.  5$\stackrel{^}{\mathrm{i}}$ N

4.  4$\stackrel{^}{\mathrm{i}}$ N

Subtopic:  Potential Energy: Relation with Force |
60%
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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/r2, where K is a constant. The total energy of the particle will be:

1. $\frac{K}{2r}$

2. $-\frac{K}{2r}$

3. $-\frac{K}{r}$

4. $\frac{K}{r}$

Subtopic:  Potential Energy: Relation with Force |
58%
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