Potential Energy

Q.

Gravitational Potential is?

Q.

The SI unit of gravitational potential is

1. $kg/Joule$

2. $Joule/k{g}^2$

3. $Joule/kg$

4. $Joul{e}^2/kg$

Q.

A rod of mass m and length l is lying on a horizontal table. The work done in making it stand vertically on one end will be

1. 

2. 

3. 

4. 

Q. The potential energy u of a particle varies with distance from a fixed origin as u=A under root xx+B where A and B are constants. The dimensions of A and are

Q. Force (in $N$) varies with position as $F=2x^2-3x-2$, Choose correct option :-

1. $x=-1/2$ is position of stable equilibrium
2. $x=2$ is position of stable equilibrium
3. $x=-1/2$ is position of unstable equilibrium
4. $x=2$ is position of neutral equilibrium

Q. The ratio of relative strength of electromagnetic force to the weak nuclear force is ?

Q. If $E$ is the emf of a cell of internal resistance $r$. It is connected with an external resistance $R$, then potential difference across $R$ is given as

1. $V=\frac{E}{(R+r)}$
2. $V=E$
3. $V=\frac{E}{(1+r/R)}$
4. $V=\frac{E}{(1+R/r)}$

Q.

Is gravitational potential a vector?

Q. A particle is placed at the origin and a force $F=kx$ is acting on it (where, $k$ is a positive constant). If $U\left(0\right)=0$, the graph of $U\left(x\right)$ versus $x$ will be (where $U$ is the potential energy function)

1. 
2. 
3. 
4. 

Q. The units of force , velocity and energy are 100 dyne, 10 cm/s, 500 erg respectively. The units of mass, length, and time are

Q.

The potential energy U in joule of a particle of mass 1 kg moving the x-y plane obeys the law U = 3x + 4y, where (x, y) are the co-ordinates of the particle in meter. If the particle is at rest at (6, 4) at time t = 0 then:

1. The particle has constant acceleration

2. The particle has zero acceleration

3. The speed of the particle when it crosses y-axis is 10 m/s

4. Co-ordinate of particle at t = 1 sec is (4.5, 2)

Q. The potential energy (in joule) of a body of mass $2\text{kg}$ moving in the $x-y$ plane is given by $U=6x+8y$, where the position coordinates $x$ and $y$ are measured in meter. If the body is at rest at point $(6m,4m)$ at time $t=0$, it will cross the y – axis at time $t$ equal to

1. $1\text{s}$
2. $3\text{s}$
3. $4\text{s}$
4. $2\text{s}$

Q. Car has a velocity of 90 km per hour when It begin to asend a hill without the help from its engine . what height will it rise before coming to rest if one third of its energy is lost in overcoming the fictional force

Q. A planet is revolving around the sun as shown in an elliptical path


The correct option is

1. The time taken in travelling DAB is less than that for BCD
2. The time taken in travelling DAB is greater than that for BCD
3. The time taken in travelling CDA is less than that for ABC
4. The time taken in travelling CDA is greater than that for ABC

Q. An object of mass $2\text{kg}$ is moved from infinity to a point $\text{P}$. Initially the object was at rest but on reaching $\text{P}$ its speed becomes $2\text{m/s}$. If the work done in moving that object is $-4\text{J}$, then find the ratio of potential energy to mass at point $\text{P}$ (in $\text{J/kg}$) is

1. $8$
2. $-8$
3. $4$
4. $-4$

Q.

The potential energy (in joule) of a body of mass 2 kg moving in the x-y plane is given by
U = 6x + 8y
where the position coordinates x and y are measured in metre. If the body is at rest at point (6 m, 4m) at time t = 0, it will cross the y-axis at time t equal to

1. 1 s

2. 2 s

3. 3 s

4. 4 s

Q. If the unit of force, energy and velocity are 100 dyne, 400 erg and 10cm/s respectively, find the unit of length, mass and time.

Q. The potential energy of a particle of mass $1kg$ is , $U=10+(x-2{)}^2$. Here $U$ is in joule and $x$ in metre on the positive x-axis. Particle travels upto $x=+6m$. Choose the appropriate answer.

1. The maximum kinetic energy of the particle is $16J$
2. Both (a) and (b) are correct
3. On negative x-axis particle travels upto $x=-2m$
4. Both (a) and (b) are wrong

Q.

A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated.
(a) How much work does she do against the gravitational force?
(b) Fat supplies $3.8\times {10}^{7}J$ of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?

Q.

An electron initially at rest is accelerated through a potential difference of $1V$. The energy gained by the electron is:

Q. If the planet moves faster when it is closer to the sun and slower when it is farther away, its instantaneous aerial velocity should change. Then how is it that the keplers second law of planetary motion state that the aerial velocity is constant?

Q. A rod of mass $m$ and length $l$ is kept near a point mass $m$ which is at a distance of $a$ from the center of the rod as shown in the figure. Find the potential energy due to the rod at point mass.

1. $U=\frac{-G{m}^2}{l}\ln \left(\frac{2a+l}{2a-l}\right)$
2. $U=\frac{-G{m}^2}{l}\ln \left(\frac{a+l}{a}\right)$
3. $U=\frac{-2G{m}^2}{l}\ln \left(\frac{2a+l}{2a-l}\right)$
4. $U=\frac{-G{m}^2}{l}\ln \left(\frac{a}{a-l}\right)$

Q.

Once a zero potential energy reference state is chosen, the changes in potential energy for a given initial and final states

1. Are same

2. Are different

3. Depend strictly on the choice of the zero of potential energy

4. Become indeterminate

Q. Gravitational potential energy is defined because gravitational force is conservative in nature.

1. True
2. False

Q. A $10kg$ ball is dropped from a height of $10m$. Find (a) the initial potential energy of the ball, (b) the kinetic energy just before it reaches the ground, and (c) the speed just before it reaches the ground.

Q. A particle of mass $m$ is projected vertically upwards from point $\Delta$ on the ground. The ratio of potential energy at point $A$ and potential energy at $B$ is

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

Q. The electric potential $V$ at any point $(x,y,z)$ in space is given by $V=3x^2$ where $x,y,z$ are all in metre. The electric field at the point $(1m,0,2m)$ is

1. $6V{m}^{-1}$ along negative $x$-axis
2. $6V{m}^{-1}$ along positive $x$-axis
3. $12V{m}^{-1}$ along positive $x$-axis
4. $12V{m}^{-1}$ along negative $x$-axis
5. $8V{m}^{-1}$ along negative $x$-axis

Q. A particle free to move along $y-$ axis has potential energy
$U\left(y\right)=k[1-e^{-y^2}]$ for $-a\le y\le a$ where $k$ is a constant. Then

1. At $y=0$, potential energy $=0$
2. At $y=\pm a$, potential energy is maximum
3. At $y=0$, kinetic energy is maximum
4. At $y=\pm a$, Kinetic energy is minimum

Q. A particle of mass $10\text{kg}$ is dropped from tower of height $10\text{m}$. Find the ratio of workdone by gravity from point ${}^{\prime }{A}^{\prime }$ to ${}^{\prime }{B}^{\prime }$ and change in potential energy from ${}^{\prime }{A}^{\prime }$ to ${}^{\prime }{B}^{\prime }$

1. $1$
2. $-1$
3. $2$
4. $16$

Q.

Statement(A): Negative charges always move from a higher potential to lower potential point.

Statement (B): Electric potential is vector.

1. A is true but B is false
2. B is true but A is false
3. Both A and B false
4. Both A and R are true