(D) The relationship between force $F$ and potential energy $U$ is given by $F = -\frac{dU}{dx}$.Therefore,$dU = -F dx$.Given $F = -2x$,we substitute

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(D) The relationship between force $F$ and potential energy $U$ is given by $F = -\frac{dU}{dx}$.Therefore,$dU = -F dx$.Given $F = -2x$,we substitute this into the equation:$dU = -(-2x) dx = 2x dx$.Integrating both sides with the condition that $U = 0$ at $x = 0$:$\int_0^U dU = \int_0^x 2x dx$.$U = [x^2]_0^x = x^2$.The potential energy function is $U = x^2$,which represents a parabola opening upwards with its vertex at the origin. This corresponds to the graph shown in option $D$.

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

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$A$ particle moves under the influence of a force $F = -2x$ in one dimension (where $x$ is the distance of the particle from the origin). Assume that the potential energy of the particle at the origin is zero. The schematic diagram of the potential energy $U$ as a function of $x$ is given by:

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Work, Energy, Power and Collision

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Potential Energy

$A$ chain of mass $m$ and length $l$ is hanging freely from edge $A$ (as shown in diagram $I$). Calculate the work done to fold it as shown in diagram $(II)$.

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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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If the potential energy of a particle of mass $0.1 \ kg$ moving along $x$-axis is $U(x) = 5x(x-4) \ J$,then the speed of the particle is maximum at a position of

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$A$ uniform chain of length $L$ and mass $M$ is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If $g$ is the acceleration due to gravity, the work required to pull the hanging part onto the table is

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$A$ uniform chain of length $l$ and mass $m$ lies on the surface of a smooth hemisphere of radius $R$ $(R > l)$ with one end tied to the top of the hemisphere as shown in the figure. Gravitational potential energy of the chain with respect to the base of the hemisphere is

DifficultAP EAMCET 2018

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$A$ particle moves under the influence of a force $F = -2x$ in one dimension (where $x$ is the distance of the particle from the origin). Assume that the potential energy of the particle at the origin is zero. The schematic diagram of the potential energy $U$ as a function of $x$ is given by:

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$A$ chain of mass $m$ and length $l$ is hanging freely from edge $A$ (as shown in diagram $I$). Calculate the work done to fold it as shown in diagram $(II)$.

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?

If the potential energy of a particle of mass $0.1 \ kg$ moving along $x$-axis is $U(x) = 5x(x-4) \ J$,then the speed of the particle is maximum at a position of

$A$ uniform chain of length $L$ and mass $M$ is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If $g$ is the acceleration due to gravity, the work required to pull the hanging part onto the table is

$A$ uniform chain of length $l$ and mass $m$ lies on the surface of a smooth hemisphere of radius $R$ $(R > l)$ with one end tied to the top of the hemisphere as shown in the figure. Gravitational potential energy of the chain with respect to the base of the hemisphere is

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