BM Sharma Solutions for Chapter: Work, Power, and Energy, Exercise 3: DPP

A particle of mass,$m=1 \mathrm{kg}$, lying on$x$-axis, experiences a force given by law, $F=x(3x-2) \mathrm{N}$, 

where $x$ is the coordinate of the particle in $\mathrm{meters}$.

(a) Locate the points on$x$-axis where the particle is in equilibrium.

(b) Draw the graph of variation of force$F$($y$-axis) with $x$-coordinate of the particle ($x$-axis). Hence or otherwise, indicate at which positions the particle is in stable or unstable equilibrium.

(c) What is the minimum speed to be imparted to the particle placed at$x=4 \mathrm{m}$ such that it reaches the origin?

The potential energy between two atoms in a molecule is given by, $U\left(x\right)=\frac{a}{x^{12}}-\frac{b}{x^6}$, where $a$ and $b$ are positive constants and $x$ is the distance between the atoms. The atoms are in stable equilibrium when,

The force acting on a body moving along $x-$axis varies with position of the particle as shown in the figure.

  The body is in stable equilibrium at

The potential energy of a particle varies with distance $x$ as shown in the graph.

The diagrams represent the potential energy$U$ as a function of the interatomic distance$r$. Which diagram corresponds to stable molecules found in nature?

One end of an unstretched vertical spring is attached to the ceiling and an object attached to the other end is slowly lowered to its equilibrium position. If $S$ be gain in spring energy and $G$ be loss in gravitational potential energy in the process then,

If the given plot shows the variation of $U$, the potential energy of interaction between two particles with the distance separating them is $r.$ Then, which of the following statements are correct.

In the figure, the variation of the potential energy of a particle of mass $m=2 \mathrm{kg}$ is represented with respect to its $x$-coordinate. The particle moves under the effect of this conservative force along the$x$-axis. Which of the following statements are correct about the particle?