PE Diagram

Q. The $F-x$ graph is shown below. Find the change in potential energy from $x=0$ to $x=5\text{m}$

1. $50\text{J}$
2. $25\text{J}$
3. $-35\text{J}$
4. $10\text{J}$

Q. The given plot shows the variation of potential energy $U$ due to the interaction between two particles. Particles are separated by a distance $r$. Identify the correct statement out of the given statements:

$1$. $B$ and $D$ are equilibrium points.
$2$. $C$ is a point of stable equilibrium.
$3$. The force of interaction between the two particles is attractive between points $B$ and $C$, and repulsive between points $D$ and $E$ on the curve.
$4$. The force of interaction between the particles is repulsive between points $A$ and $C$.
Which of the above statements are correct?

1. $1$ and $3$
2. $1$ and $4$
3. $2$ and $4$
4. $2$ and $3$

Q. which of the fpollowing graphs show the variation of Potential Energy of a body if it is taken to a height h and dropped from there?

1. 
2. 
3. 
4. 

Q. Potential energy of a particle is given by $U=(2-3x-4x^2)\text{J}$ where '$x$' is in '$m$'. Find the magnitude of force at $x=4\text{m}$, if the particle is free to move along $x$-direction.

1. $29\text{N}$
2. $35\text{N}$
3. $16\text{N}$
4. $18\text{N}$