Potential Energy

A particle in a certain conservative force field has a potential energy given by $U=\frac{20xy}{z}$. The force exerted on it is

A uniform chain of length $2 \mathrm{m}$ is kept on a table such that a length of $60 \mathrm{cm}$ hangs freely from the edge of the table. The total mass of the chain is $4 \mathrm{kg}$. What is the work done in pulling the entire chain in the table?

A particle is moved from $\left(0, 0\right)$ to $\left(a, a\right)$ under a force $F=(3\hat{\mathrm{i}}+4\hat{\mathrm{j}})$ from two paths. Path $1$ is $OP$ and path $2$ is $OQP$. Let $W_1$ and $W_2$ be the work done by this force in these two paths. Then,

If $W_1, W_2$ and $W_3$ represent the work done in moving a particle from $A$ to $B$ along three different paths $1, 2$ and $3$, respectively (as shown), in the gravitational field of a point mass $m$, find the correct relation between $W_1, W_2$ and $W_3$.

A spring $40 \mathrm{mm}$ long is stretched by the application of a force. If $10 \mathrm{N}$ force required to stretch the spring through $1 \mathrm{mm}$, then work done in stretching the spring through $40 \mathrm{mm}$ is

Potential energy and displacement curve is given in diagram.

The force at $x=5 \mathrm{m}$ is

A block of mass $M$ moving on the frictionless horizontal surface collides with a spring of spring constant $k$ and compresses it by length $L.$ The maximum momentum of the block is

The spring constant of the spring of a gun is $k$ newton/meter. The spring has been compressed $x$ meter from its normal position and a bullet of mass $m$ has been put in the barrel. If the friction is negligible then on firing the gun, the bullet shall have a velocity of $\left(\mathrm{m}/\sec \right):$

The spring extends by $x$ on loading, then energy stored by the spring is : (If $T$ is the tension in spring and $k$ is spring constant)

A point particle with maximum kinetic energy very slightly less than $9 \mathrm{J}$ moves in a potential field shown in the figure. Then the approximate time period of oscillation of the particle is $($mass $=2 \mathrm{kg})$

A particle is moving on $x$ -axis has potential energy $U=\left(2-20x+5x^2\right)$ joules along $x$-axis. The particle is released at $x=-3 .$ The maximum value of $\text{'}x\text{'}$ will be [$x$ is in meters and $U$ is in joules]:

From a fixed support $\mathrm{O}$, hangs an elastic string of negligible mass and natural length $L$. Masses $m_1$ and $m_2$ attached at the lower end, elongate the string to $2 \mathrm{L}$. When $m_2$ is removed gently, $m_1$ is able to bounce back to $\mathrm{O}$. The ratio $m_2/m_1$ is (assume that the string does not obstruct the motion of $m_1$ )

Two springs of spring constants $1500 \mathrm{N} {\mathrm{m}}^{-1}$ and $3000 \mathrm{N} {\mathrm{m}}^{-1}$ respectively are stretched with the same force. They will have potential energy in the ratio-

The figure below shows a graph of potential energy $U\left(x\right)$ verses position $x$ for a particle executing one dimensional motion along the $x$-axis. The total mechanical energy of the system is indicated by the dashed line. At $t=0$ the particle is somewhere between points $\mathrm{A}$ and $\mathrm{G}$. For later times, choose the correct statement :-

Calculate the force $F\left(y\right)$ associated with the following one-dimensional potential energy :-

$U=a{y}^3-b{y}^2$

An elastic string of unstretched length $l$ and force constant $k$ is stretched by a small length $\mathit{x}\mathit{.}$ It is further stretched by another small length $y$. The work done in the second stretching is :-

The force acting on a body moving along $\mathrm{x}-$axis varies with the position of the particle shown in the figure. The body is in stable equilibrium at

Select the correct Potential energy($U$) vs inter-atomic distance($r$) for a stable molecules found in nature.

In the given graph shown the variation of the potential energy U by the interaction between two particles, with the distance separating them, $r$.

(i) $C$ is a point of stable equilibrium
(ii) $B$ and $D$ equilibrium points
(iii) The force of interaction between the particles is repulsive between points $C$ and $A$.
(iv) The force of interaction between the two particles is attractive between points $C$ and $B$, and repulsive between $D$ and $E$ on the curve
Choose correct statement(s)?

A particle of mass $5 \mathrm{kg}$ moving in the $\mathrm{x}-\mathrm{y}$ plane has its potential energy given by $\mathrm{U} = (-7\mathrm{x}+24\mathrm{y}) \mathrm{Joule}$, $x$ and $y$ being in $\mathrm{meter}$. Initially at $\mathrm{t} =0$,the particle is located at the origin $(0, 0)$ and moving with a velocity of  $6\left[2.4\hat{i}+0.7\hat{j}\right] \mathrm{m}/\mathrm{s}$ . Find the magnitude of force acting on the particle.