The graphs below shows the force acting on a particle when it moves along the positive $x$-axis from the origin to $x=x_1.$ The force is parallel to the $x$-axis and is conservative. The maximum magnitude $F_1$ has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force, least (or most negative) to greatest (or most positive)

A particle is released from rest at the point $x=a$ and moves along the $x$-axis subject to the potential energy function $U\left(x\right)$ shown. The particle

The diagram shows a plot of the potential energy as a function of $x$ for a particle moving along the $x$-axis. The points of stable equilibrium are

The first graph shows the potential energy $U\left(x\right)$ for a particle moving on the $x$-axis. Which of the following five graphs correctly gives the force $F$ exerted on the particle?

The string in the figure is $50 \mathrm{cm}$ long. When the ball is released from rest, it will swing along the dotted arc. How fast, in $\mathrm{m} {\mathrm{s}}^{–1},$ will it be going at the lowest point in its swing?

A ball of mass $m,$ at one end of a string of length $L,$ rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. The speed of the ball at the bottom of the circle is

When a block of mass $\text{'}m\text{'}$ is released from point $\text{'}A\text{'}$ on the surface of a smooth bowl, the normal reaction force on it at the lowest point would be equal to