Potential Energy

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. A ladder (uniform) is inclined at ${37}^{\circ }$ with horizontal (zero level). Potential energy of the rod is

1. 48 J
2. 124 J
3. 96 J
4. 132 J

Q. If two electric bulbs one of $200V-40W$ and other of $200V-100W$ are connected in a domestic circuit, then

1. They have equal resistance
2. The resistance of $100W$ bulb is more than $40W$ bulb
3. They have equal current passing through them
4. The resistance of $40W$ bulb is more than $100W$ bulb

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.

A body at rest may have

1. Energy

2. Momentum

3. Speed

4. Velocity

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

Q.

A liquid of density d is pumped by a pump p from situation (i) to situation (ii) as shown in the diagram. If the cross-section of each of the vessels is a, then the work done in pumping (neglecting friction effects) is

1. $2dgh$

2. $dgha$

3. $2dg{h}^{2}a$

4. $dg{h}^{2}a$

Q. If two electric bulbs one of $200V-40W$ and other of $200V-100W$ are connected in a domestic circuit, then

1. They have equal resistance
2. The resistance of $100W$ bulb is more than $40W$ bulb
3. They have equal current passing through them
4. The resistance of $40W$ bulb is more than $100W$ bulb

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. The mass of a spaceship is $1000\text{kg}$. It is to be launched from the earth's surface out into free space. The value of $g$ and $R$ (radius of earth) are $10{\text{m/s}}^2$ and $6400\text{Km}$ respectively. The required energy for this work will be

1. $6.4\times {10}^9$ $\text{J}$
2. $6.4\times {10}^8$ $\text{J}$
3. $6.4\times {10}^{10}$ $\text{J}$
4. $6.4\times {10}^{11}$ $\text{J}$

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