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Standard XI

Physics

Conservative Force as Gradient of Potential

A plot of pot...

Question

A plot of potential energy function $U (x) = k x^{2}$ , where $x$ is the displacement and $k =$ constant is shown below. The correct conservative force function $F (x)$ is

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Solution

The correct option is A
$∵$ The relation of conservative force function is given by $F = - d U / d x$
Now, given that $U (x) = k x^{2}$
$⟹ F = - 2 k x$ ,
which means $F \propto - x$ .
Also at $x = 0$ , $F = 0$ $\Rightarrow$ graph passes through the origin.

Option (a) is the correct graph.

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A plot of potential energy function U(x)=kx2, where x is the displacement and k= constant is shown below. The correct conservative force function F(x) is

The correct option is A ∵ The relation of conservative force function is given by F=−dU/dx Now, given that U(x)=kx2 ⟹F=−2kx, which means F∝−x. Also at x=0, F=0 ⇒ graph passes through the origin. Option (a) is the correct graph.

A plot of potential energy function $U (x) = k x^{2}$ , where $x$ is the displacement and $k =$ constant is shown below. The correct conservative force function $F (x)$ is

The correct option is A
$∵$ The relation of conservative force function is given by $F = - d U / d x$
Now, given that $U (x) = k x^{2}$
$⟹ F = - 2 k x$ ,
which means $F \propto - x$ .
Also at $x = 0$ , $F = 0$ $\Rightarrow$ graph passes through the origin.

Option (a) is the correct graph.