(B) For a conservative force,$F = -\frac{dU}{dx} = -(2ax - b) = -2ax + b$. At the equilibrium position,$F = 0$,so $-2ax + b = 0$,which gives $x = \fra

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$\frac{b}{2a}, -\frac{b^2}{4a}$

(B) For a conservative force,$F = -\frac{dU}{dx} = -(2ax - b) = -2ax + b$. At the equilibrium position,$F = 0$,so $-2ax + b = 0$,which gives $x = \frac{b}{2a}$. The equilibrium potential energy is $U = a(\frac{b}{2a})^2 - b(\frac{b}{2a}) = \frac{b^2}{4a} - \frac{b^2}{2a} = -\frac{b^2}{4a}$.

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

Medium

For a system of conservative forces,the potential energy is given by the formula $U = ax^2 - bx$,where $a$ and $b$ are constants. The equilibrium position and the equilibrium potential energy will be,respectively:

A
$\frac{b}{2a}, -\frac{b}{2a}$
B
$\frac{b}{2a}, -\frac{b^2}{4a}$
C
$\frac{b^2}{2a}, -\frac{b^2}{2a}$
D
$-\frac{b}{4a}, -\frac{b}{4a}$

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Work, Energy, Power and Collision

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Potential Energy

$A$ body at rest may have

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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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Calculate the work done in rotating a vertical meter scale of mass $400 \, g$ by an angle of ${60^o}$. (in $, J$)

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The potential energy of a particle in a central field has the form $U(r) = \frac{1}{r^2} - \frac{1}{r}$,where '$r$' is the distance from the centre of the field. The magnitude of the maximum attractive force in Newton is

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For a system of conservative forces,the potential energy is given by the formula $U = ax^2 - bx$,where $a$ and $b$ are constants. The equilibrium position and the equilibrium potential energy will be,respectively:

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$A$ body at rest may have

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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