PE Diagram

Q. Given below is the plot of a potential energy function $U\left(X\right)$ for a system, in which a particle is in one dimenstional motion, while a conservative force $F\left(X\right)$ acts on it. Suppose that $E_{mech}=8\text{J}$, the incorrect statement for this system is :

1. at $X>X_4$, K.E. is constant throughout the region.
2. at $X<X_1$, K.E. is smallest and the particle is moving at the slowest speed.
3. at $X=X_2$, K.E. is greatest and the particle is moving at the fastest speed.
4. at $X=X_3$, K.E $=4\text{J}.$

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. The potential energy $U$ between two molecules as a function of the distance $X$ between them has been shown in the figure. The two molecules are

1. attracted when $X$ lies between $A$ and $B$ and are repelled when $X$ lies between $B$ and $C$
2. attracted when $X$ lies between $B$ and $C$ and are repelled when $X$ lies between $A$ and $B$
3. attracted when they reach $B$
4. repelled when they reach $B$

Q. Four equal charges $+q$ are placed at four corners of a square with its center as origin and lying in $\text{yz}$ plane. The electrostatic potential energy of a fifth charge $+q$ varies on $\text{x-}$axis as

1. 
2. 
3. 
4. 

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

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

Q. A particle is acted by a force F = kx, where k is a positive constant. Its potential energy at x = 0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x

1. 
2. 
3. 
4. 

Q. If the total energy of th eparticle is $E$, it will perform periodic motion only if

1. $V_0>E>0$
2. $E<0$
3. $E>0$
4. $E>V_0$

Q. A potential energy function for a two dimensional force is of the form $U=9x^{3}y-12x$. Find conservative force at point (1, 2).

1. $-42\hat{i}-9\hat{j}$
2. $-36\hat{i}+18\hat{j}$
3. $-18\hat{i}+9\hat{j}$
4. None

Q. The potential difference between two points $A$ and $B$ is

1. Zero
2. $\frac{Q}{4\pi {ϵ}_{0}a}(1-\frac{1}{\sqrt{5}})$
3. $\frac{Q}{4\pi {ϵ}_{0}a}[2-\frac{1}{\sqrt{5}}]$
4. $\frac{Q}{2\pi {ϵ}_{0}a}[1-\frac{1}{\sqrt{5}}]$

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. $18\text{N}$

Q. A mass $2\text{kg}$ is moved from point $\text{A}$ to $\text{B}$. If the increase in kinetic energy of mass is $4\text{J}$ and work done on the mass is $-10\text{J}$, then potential difference between $\text{B}$ and $\text{A}$ ($\text{J/kg}$) is

1. $4$
2. $7$
3. $-3$
4. $-7$

Q. The potential energy for a force field $\overrightarrow{F}$ is given by $U(x,y)=\sin (x+y)$. The force acting on the particle of mass $m$ at $(0,\frac{\pi }{4})$ is (in $N$)

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

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. The given plot shows the variation of U, the potential energy of interaction between two particles with the distance separating them r.

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 C and D and repulsive between D and E
4. The force of interaction between particles is repulsive between points E and F.

The correct statements are:

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

Q. A conservative force of $\overrightarrow{F}=(-3\hat{i})N$ acts on a body of mass 3 kg. The change in potential energy of the body due to the force, when it undergoes a displacement $6\hat{i}m$ is

3 kg द्रव्यमान के एक पिण्ड पर एक संरक्षी बल $\overrightarrow{F}=(-3\hat{i})N$ क्रियाशील है। जब पिण्ड $6\hat{i}m$ विस्थापित होता है, तब बल के कारण पिण्ड की स्थितिज ऊर्जा में परिवर्तन है

1. 18 J
2. 21 J
3. 24 J
4. 19 J

Q. The potential energy for a force field $\overrightarrow{F}$ is given by $U(x,y)=\sin (x+y)$. The force acting on the particle of mass $m$ at $(0,\frac{\pi }{4})$ is (in $N$)

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

Q. A potential energy function for a two-dimensional force is of the form $U=3x^{2}y-7x$. Find the force that acts at the point (x, y).

Q. The given plot shows the variation of U, the potential energy of interaction between two particles with the distance separating them be $r$, then which of the following is correct?
(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 C and D and repulsive between points D and E on the curve.
(4) The force of interaction between the particles is repulsive between points E and F on the curve.

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

Q. Potential energy curve $U$ of a particle as function of the position of a particle is shown. The particle has total mechanical energy $E$ of $3.0$ joules. Then select correct alternative.

1. At $x=1$ its kinetic energy $3J$
2. It can never be present at $x=0m$
3. It can never be present at $x=5m$
4. At $x=2$ its kinetic energy of $0J$

Q. A particle is acted by a force F = kx, where k is a positive constant. Its potential energy at x = 0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x

1. 
2. 
3. 
4. 

Q. The potential energy of a particle of mass 5kg moving in xy-plane is given as
$U=(7x+24y)$ joule, $x$ and $y$ being in meter. Initially at $t=0$, the particle is at the origin $(0,0)$ moving with a velocity of $(8.6\hat{i}+23.2\hat{j})m{s}^{-1}$. Then

1. The velocity of the particle at $t=4s$, is $5m{s}^{-1}$
2. The acceleration of the particle is $5m{s}^{-2}$
3. The direction of motion of the particle initially (at $t=0$) is at right angle to the direction of acceleration
4. The path of the particle is circle

Q. The potential energy U between two molecules as a function of the distance X between then has been shown in the figure. The two molecules are

1. Repelled when they reach B
2. Attracted when x lies between A and B and are repelled when X lies between B and C
3. Attracted when they reach B
4. Attracted when x lies between B and C and are repelled when X lies between A and B

Q. The potential energy of a certain particle is given by $U=\frac{1}{2}(x^2-z^2)$. The force on it is

1. $-x\hat{i}+z\hat{k}$
2. $x\hat{i}+z\hat{k}$
3. $\frac{1}{2}(x\hat{i}+z\hat{k})$
4. $\frac{1}{2}(x\hat{i}-z\hat{k})$

Q.

Fig. Shows a plot of the conservation force F in a unidimensional field. The plot representing the function corresponding to the potential energy (U) in the fields is

1. 

2. 

3. 

4. 

Q. The potential energy for a force field $\overrightarrow{F}$ is given by $U(x,y)=\sin (x+y)$. The force acting on the particle of mass $m$ at $(0,\frac{\pi }{4})$ is (in $N$)

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

Q. A potential energy function for a two dimensional force is of the form $U=9x^{3}y-12x$. Find conservative force at point (1, 2).

1. $-42\hat{i}-9\hat{j}$
2. $-36\hat{i}+18\hat{j}$
3. $-18\hat{i}+9\hat{j}$
4. None

Q. The potential energy for a force field $\overrightarrow{F}$ is given by U(x, y) = sin(x + y). Magnitude of the force acting on the particle of mass m at $(0,\frac{\pi }{4})$ is

1. 1
2. $\sqrt{2}$
3. $\frac{1}{\sqrt{2}}$
4. 0

Q. The potential energy of a body is given by $U=A-{Bx}^2$ (where x is the displacement). The magnitude of force acting on the particle is

1. Constant
2. Proportional to $x$
3. Proportional to $x^2$
4. Inversely proportional to $x$

Q.

Fig. Shows a plot of the conservation force F in a unidimensional field. The plot representing the function corresponding to the potential energy (U) in the fields is

1. 

2. 

3. 

4. 

Q. A potential energy function for a two dimensional force is of the form $U=9x^{3}y-12x$. Find conservative force at point (1, 2).

1. $-18\hat{i}+9\hat{j}$
2. None
3. $-36\hat{i}+18\hat{j}$
4. $-42\hat{i}-9\hat{j}$