Potential Energy Is Defined for a System

Q. Two identical thin rings each of radius R meters are coaxially placed at a distance R meters apart. If $Q_1$ coulomb and $Q_2$ coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of other is

1. Zero
2. $\frac{q(Q_2-Q_1)(\sqrt{2}-1)}{\sqrt{2}.4\pi {ϵ}_{0}R}$
3. $\frac{q\sqrt{2}(Q_1+Q_2)}{4\pi {ϵ}_{0}R}$
4. $\frac{q(Q_1+Q_2)(\sqrt{2}+1)}{\sqrt{2}.4\pi {ϵ}_{0}R}$

Q. A uniformly charged finite rod is placed along $x-$axis, as shown in the figure. At point $P$, find the angle made by $\overrightarrow{E}$ with $x-$direction.

1. ${45}^{\circ }$
2. ${\tan }^{-1}\left(\frac{2}{3}\right)$
3. ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$
4. None of these
   

Q. Two concentric spheres of radii $R$ and $2R$ are charged. The inner sphere has a charge of $1\mu \text{C}$ and the outer sphere has a charge of $2\mu \text{C}$ of the same sign. The potential is $9000\text{V}$ at a distance $3R$ from the common centre. The value of $R$ is

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

Q. what is surface energy

Q.

Statement 1: Potential energy depends on the choice of reference point.

Statement 2: Change in potential energy depends upon the choice of reference point.

1. Statement 1 is false, statement 2 is true.
2. Statement 1 is false, statement 2 is false.
3. Statement 1 is true, statement 2 is true.
4. Statement 1 is true, statement 2 is false.

Q. An aluminium rod has a breaking strain of 0.2% the minimum cross sectionall area of the rod in square meter in order to support a load of 10power4N is if youngs modulls is 7×10power9 N/square metres

Q. Two bodies of masses 100kg and 1000kg are at a distance of 1m apart. Calculate the gravitational field intensity and potential at the middle point of line joining them.(G=6.67*10 ^-11)

Q. Two electrostatic field lines are drawn between two point charges $q_1\&q_2$ as shown in the diagram , If $\alpha \&\beta$ are planar angles. then the ratio $q_1/q_2$ will be

1. 
   $\frac{\sin \left(\alpha /2\right)}{\sin \left(\beta /2\right)}$
2. 
   $\frac{{\sin }^2\left(\alpha /2\right)}{{\sin }^2\left(\beta /2\right)}$
3. 
   $\frac{{\sin }^2\left(\beta /2\right)}{{\sin }^2\left(\alpha /2\right)}$
4. 
   $\frac{\cos \beta }{\cos \alpha }$

Q. A mass $m$ is hanging from a wire of cross-sectional area $A$ and length $L.Y$ is young's modulus of wire. An external force $F$ is applied on the wire which is then slowly further pulled down by $\Delta x$ from its equilibrium position. Find the work done by the force $F$ the wire exerts on the mass.

1. $mg\Delta x+\frac{YA{\left(\Delta x\right)}^2}{L}$
2. $mg\Delta x+\frac{YA}{2L}{\left(\Delta x\right)}^2$
3. $mg\frac{\Delta x}{2}+\frac{YA{\left(\Delta r\right)}^2}{2L}$
4. $mg\frac{\Delta x}{2}+\frac{YA{\left(\Delta x\right)}^2}{L}$

Q. The work done by all the forces (external and internal) on a system equals the change in
(a) total energy
(b) kinetic energy
(c) potential energy
(d) none of these

Q. Two equal negative charges $-q$ each are fixed at points $(0,-a)$ and $(0,a)$ on y-axis. A positive charge $Q$ is released from rest at the point $(2a,0)$ on the $x$ - axis. The charge $Q$ will

1. execute simple harmonic motion about the origin
2. move to the origin and remain at rest
3. move to infinity
4. execute oscillatory but not simple harmonic motion

Q.

When you lift an apple from a table to your mouth to enjoy its deliciousness, then

1. P.E of Earth-apple system increases
2. P.E of Earth-apple system decreases.

3. P.E of the apple increases.

4. P.E of Earth decreases

Q. The negative of the work done by a conservative internal force of a system equals the change in its

1. Total energy
2. Kinetic energy
3. Potential energy
4. None of these

Q. Two equal negative charges $-q$ each are fixed at points $(0,-a)$ and $(0,a)$ on y-axis. A positive charge $Q$ is released from rest at the point $(2a,0)$ on the $x$ - axis. The charge $Q$ will

1. execute simple harmonic motion about the origin
2. move to the origin and remain at rest
3. move to infinity
4. execute oscillatory but not simple harmonic motion

Q. If the P.E of a system decreases by 40 J while the K.E remains constant, then the work done by external agent will be.

1. 40 J
2. -40 J
3. 20 J
4. 0 J

Q.

Statement 1: Potential energy depends on the choice of reference point.

Statement 2: Change in potential energy depends upon the choice of reference point.

1. Statement 1 is true, statement 2 is true.
2. Statement 1 is true, statement 2 is false.
3. Statement 1 is false, statement 2 is true.
4. Statement 1 is false, statement 2 is false.

Q. Two identical thin rings each of radius R meters are coaxially placed at a distance R meters apart. If $Q_1$ coulomb and $Q_2$ coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of other is

1. Zero
2. $\frac{q(Q_2-Q_1)(\sqrt{2}-1)}{\sqrt{2}.4\pi {ϵ}_{0}R}$
3. $\frac{q\sqrt{2}(Q_1+Q_2)}{4\pi {ϵ}_{0}R}$
4. $\frac{q(Q_1+Q_2)(\sqrt{2}+1)}{\sqrt{2}.4\pi {ϵ}_{0}R}$

Q. A particle of mass $1\times {10}^{-26}kg$ and charge $+1.6\times {10}^{-19}C$ travelling with a velocity $1.28\times {10}^{6}m{s}^{-1}$ in the +x direction enters a region in which uniform electric field E and a uniform magnetic field of induction B are present such that $E_x=E_y=0,E_z=-102.4kV{m}^{-1}$, and $B_x=B_z=0,B_y=8\times {10}^{-2}$. The particle enters this region at time $t=0$. Determine the location (x, y, z coordinates) of the particle as $t=5\times {10}^{-6}s$. If the electric field is switched off at this instant (with the magnetic field present), what will be the position of the particle at $t=7.45\times {10}^{-6}s$?

Q. Two identical thin rings each of radius R meters are coaxially placed at a distance R meters apart. If $Q_1$ coulomb and $Q_2$ coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of other is

1. Zero
2. $\frac{q(Q_2-Q_1)(\sqrt{2}-1)}{\sqrt{2}.4\pi {ϵ}_{0}R}$
3. $\frac{q\sqrt{2}(Q_1+Q_2)}{4\pi {ϵ}_{0}R}$
4. $\frac{q(Q_1+Q_2)(\sqrt{2}+1)}{\sqrt{2}.4\pi {ϵ}_{0}R}$

Q. Classify each of the following statements as a characteristic.
The force exerted on a charged object cannot alter the object’s speed.

1. of electric forces only
2. of magnetic forces only,
3. of both electric and magnetic forces, or
4. of neither electric nor magnetic forces.

Q. The plastic rod forms a quarter-circle of radius $R$ and has uniform charge density $+\lambda$. Find the electric field at the origin.
$k=\frac{1}{4\pi {ϵ}_0}$

1. $\frac{k\lambda }{r}$
2. $\frac{\sqrt{2}k\lambda }{r}$
3. $\frac{2k\lambda }{r}$
4. $\frac{\sqrt{3}k\lambda }{r}$

Q.

Statement 1: Potential energy depends on the choice of reference point.

Statement 2: Change in potential energy depends upon the choice of reference point.

1. Statement 1 is true, statement 2 is true.
2. Statement 1 is true, statement 2 is false.
3. Statement 1 is false, statement 2 is true.
4. Statement 1 is false, statement 2 is false.

Q.

Choose the correct alternative:

(a) If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic/potential energy.

(b) The energy required to launch an orbiting satellite out of earth’s gravitational influence is more/less than the energy required to project a stationary object at the same height (as the satellite) out of earth’s influence.

Q. Surface energy:-