(A) The force components are derived from the negative gradient of the potential energy: $F_x = -\frac{\partial U}{\partial x} = -a$ $F_y = -\frac{\pa

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(A) The force components are derived from the negative gradient of the potential energy: $F_x = -\frac{\partial U}{\partial x} = -a$ $F_y = -\frac{\partial U}{\partial y} = -b$ The magnitude of the net force $F$ is given by: $F = \sqrt{F_x^2 + F_y^2} = \sqrt{(-a)^2 + (-b)^2} = \sqrt{a^2 + b^2}$ Using Newton's second law,the acceleration $a_{acc}$ is: $a_{acc} = \frac{F}{m} = \frac{\sqrt{a^2 + b^2}}{m} = \frac{(a^2 + b^2)^{1/2}}{m}$

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

Difficult

The potential energy of a body of mass $m$ is given by $U = ax + by$,where $x$ and $y$ are the position coordinates of the particle. The acceleration of the particle is:

A
$\frac{(a^2 + b^2)^{1/2}}{m}$
B
$\frac{a^2 + b^2}{m}$
C
$\frac{(a + b)^{1/2}}{m}$
D
$\frac{a + b}{m}$

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Work, Energy, Power and Collision

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Potential Energy

The diagrams represent the potential energy $U$ as a function of the inter-atomic distance $r$. Which diagram corresponds to stable molecules found in nature?

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$A$ uniform cable of mass $M$ and length $L$ is placed on a horizontal surface such that its $(1/n)^{th}$ part is hanging below the edge of the surface. To lift the hanging part of the cable up to the surface,the work done should be

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If a body of mass $200\, g$ falls from a height $200\, m$ and its total $P.E.$ is converted into $K.E.$ at the point of contact of the body with the earth's surface,then what is the decrease in $P.E.$ of the body at the contact? $(g = 10\, m/s^2)$ ............ $J$

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For the stability of a physical system,what should be its potential energy? Should it be more or less?

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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 of a body of mass $m$ is given by $U = ax + by$,where $x$ and $y$ are the position coordinates of the particle. The acceleration of the particle is:

Similar Questions

The diagrams represent the potential energy $U$ as a function of the inter-atomic distance $r$. Which diagram corresponds to stable molecules found in nature?

$A$ uniform cable of mass $M$ and length $L$ is placed on a horizontal surface such that its $(1/n)^{th}$ part is hanging below the edge of the surface. To lift the hanging part of the cable up to the surface,the work done should be

If a body of mass $200\, g$ falls from a height $200\, m$ and its total $P.E.$ is converted into $K.E.$ at the point of contact of the body with the earth's surface,then what is the decrease in $P.E.$ of the body at the contact? $(g = 10\, m/s^2)$ ............ $J$

For the stability of a physical system,what should be its potential energy? Should it be more or less?

$A$ 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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