(D) The condition for stable equilibrium is that the net force $F$ acting on the system must be zero,where $F = -\frac{dU}{dx} = 0$.Given $U(x) = ax^{

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(D) The condition for stable equilibrium is that the net force $F$ acting on the system must be zero,where $F = -\frac{dU}{dx} = 0$.Given $U(x) = ax^{-12} - bx^{-6}$.Differentiating with respect to $x$:$\frac{dU}{dx} = -12ax^{-13} - (-6bx^{-7}) = -12ax^{-13} + 6bx^{-7}$.Setting the force to zero:$F = -(-12ax^{-13} + 6bx^{-7}) = 0$$12ax^{-13} - 6bx^{-7} = 0$$\frac{12a}{x^{13}} = \frac{6b}{x^7}$$\frac{12a}{6b} = \frac{x^{13}}{x^7}$$\frac{2a}{b} = x^6$$x = \sqrt[6]{\frac{2a}{b}}$.

Class 11 Physics Work, Energy, Power and Collision Potential Energy

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

AIPMT 1995 All AIPMT

A
$x = \sqrt[6]{\frac{11a}{5b}}$
B
$x = \sqrt[6]{\frac{a}{2b}}$
C
$x = 0$
D
$x = \sqrt[6]{\frac{2a}{b}}$

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$A$ body at rest may have

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The potential energy of a particle is given by $U = A - Bx^2$,where $x$ is the displacement. What is the magnitude of the force acting on the particle?

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The potential energy of a particle oscillating along the $x-$axis is given by $U = 20 + (x - 2)^2$,where $U$ is in joules and $x$ is in meters. The total mechanical energy of the particle is $36\,J$. The maximum kinetic energy of the particle is ................ $J$.

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The following figure shows the variation of potential energy $V(x)$ of a particle with distance $x$. The particle has

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$A$ chain of mass $M$ and length $L$ is placed on a smooth table such that $1/n$ of its length is hanging over the edge of the table. The hanging part of the chain is pulled back onto the surface of the table. Find the work done to pull it up.

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

Similar Questions

$A$ body at rest may have

The potential energy of a particle is given by $U = A - Bx^2$,where $x$ is the displacement. What is the magnitude of the force acting on the particle?

The potential energy of a particle oscillating along the $x-$axis is given by $U = 20 + (x - 2)^2$,where $U$ is in joules and $x$ is in meters. The total mechanical energy of the particle is $36\,J$. The maximum kinetic energy of the particle is ................ $J$.

The following figure shows the variation of potential energy $V(x)$ of a particle with distance $x$. The particle has

$A$ chain of mass $M$ and length $L$ is placed on a smooth table such that $1/n$ of its length is hanging over the edge of the table. The hanging part of the chain is pulled back onto the surface of the table. Find the work done to pull it up.

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