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If both the objects have the same PE curve as shown in the figure, then:
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A. For objects having total energy $E_{2}$ all values of $r$ are possible
B. For the object having total energy $E_{2}$, values of $rC. For the object having total energy $E_{1}$, all values of $r$ are possible
D. None of the above

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Last updated date: 13th Jun 2024
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Answer
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Hint: Potential energy is energy that is stored in an object or substance or conserved. This stored energy is based on the object or substance's position, arrangement or state. You can think of it as the 'potential energy to do work. Potential energy, like a spring or the force of gravity, is often associated with restoring forces.

Complete solution:
When it is converted to kinetic energy, potential energy becomes useful. For performing work, kinetic energy is used. When force is applied to an object, work occurs. Kinetic energy is useful because it makes it possible to do work. . An external force that operates against the force field of the potential performs the action of stretching a spring or lifting a mass.
At $\mathrm{r}=\mathrm{r}_{0}, \mathrm{TE}=\mathrm{E}_{1}$
$\mathrm{E}_{1}=\mathrm{TE}=\mathrm{PE}<0$
$\therefore \mathrm{KE}=0$
for $\mathrm{r}<\mathrm{r}_{0}$
$\mathrm{E}_{1}-\mathrm{PE}=\mathrm{KE}>0$
as $|\mathrm{PE}|>\left|\mathrm{E}_{1}\right|$
but for $\mathrm{r}>\mathrm{r}_{0}$
$\mathrm{KE}<0$ i.e impossible

So all values of $\mathrm{r}$ are impossible for $\mathrm{TE}=\mathrm{E}_{1}$.
Now;
for $\mathrm{TE}=\mathrm{E}_{2}$
at $\mathrm{r}<\mathrm{r}_{0}$
$\mathrm{KE}=\mathrm{E}_{2}-\mathrm{PE}>0$
as $\mathrm{PE}<0, \mathrm{E}_{2}>0$
and at $\mathrm{r} \geq \mathrm{r}_{0}$
$\mathrm{KE}=\mathrm{E}_{1}-\mathrm{PE}>0$
as $\mathrm{PE}<0, \mathrm{E}_{2}>0$
so, for $\mathrm{TE}=\mathrm{E}_{2}$ all values of $(\mathrm{r})$ are possible

Hence, option (A) is the correct Answer.

Note:
Potential energy is one of several energy types that can be possessed by an object. We will concentrate on gravitational energy, although there are several sub-types of potential energy. Potential energy is the energy due to the position of an object relative to other objects. An external force that operates against the force field of the potential performs the action of stretching a spring or lifting a mass. Potential energy is one of several energy types that can be possessed by an object. While multiple sub-types of potential energy exist,