Comparing Coulomb's Constant and Gravitational Constant

Q.

Check that the ratio $k{e}^2/G{m}_e{m}_p$ is dimensionless. Look up a table of physical constants and determine the value of this ratio. What does the ratio signify?

Q. A total charge $Q$ is broken in two parts $Q_1$ and $Q_2$ and they are placed at a distance $R$ from each other. The maximum force of repulsion between them will occur, when

1. $Q_2=\frac{Q}{R},Q_1=Q-\frac{Q}{R}$
2. $Q_2=\frac{Q}{4},Q_1=Q-\frac{2Q}{3}$
3. $Q_2=\frac{Q}{4},Q_1=\frac{3Q}{4}$
4. $Q_1=\frac{Q}{2},Q_2=\frac{Q}{2}$

Q. If $E,M,l$ and $G$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of $P$ in the formula $P=E{l}^2{M}^{-5}{G}^{-2}$ are

1. $\left[M^1{L}^1{T}^{-2}\right]$
2. $\left[M^0{L}^0{T}^0\right]$
3. $\left[M^{-1}{L}^{-1}{T}^2\right]$
4. $\left[M^0{L}^1{T}^0\right]$

Q. Three point charges of $1\text{C},2\text{C}$ and $3\text{C}$ are placed at the corners of an equilateral triangle of side $1\text{m}$. The work required to move these charges to the corners of a smaller equilateral triangle of side $0.5\text{m}.$ is $x\times {10}^9\text{J}$, Find $x$

Q. Five point charges each $+q$ are placed on five vertices of a regular hexagon of side $a$ unit. What is the magnitude of force experienced by a charge $-q$ placed at the centre of the hexagon ?

1. Zero
2. $\frac{q^2}{4\pi {ϵ}_0{a}^2}$
3. $\frac{q^2}{\sqrt{2}\pi {ϵ}_0{a}^2}$
4. $\frac{q^2}{8\pi {ϵ}_0{a}^2}$

Q. Four charges each equal to $Q$ are placed at the four corners of a square and a charge $q$ is placed at the centre of the square. If the system is in equilibrium, the value of $q$ is :

1. $\frac{Q}{2}(1+2\sqrt{2})$
2. $\frac{-Q}{4}(1+2\sqrt{2})$
3. $\frac{Q}{4}(1+2\sqrt{2})$
4. $\frac{-Q}{2}(1+2\sqrt{2})$

Q. A total charge Q is broken in two parts $Q_1$ and $Q_2$ and they are placed at a distance R from each other. The maximum force of repulsion between them will occur, when

1. $Q_2=\frac{Q}{R},Q_1=Q-\frac{Q}{R}$
2. $Q_2=\frac{Q}{4},Q_1=Q-\frac{2Q}{3}$
3. $Q_2=\frac{Q}{4},Q_1=\frac{3Q}{3}$
4. $Q_1=\frac{Q}{2},Q_2=\frac{Q}{2}$

Q. A total charge $Q$ is broken in two parts $Q_1$ and $Q_2$ , and they are placed at a distance $R$ from each other. The maximum force of repulsion between them will occur when

1. $Q_2=\frac{Q}{R},Q_1=Q-\frac{Q}{R}$
2. $Q_2=\frac{Q}{3},Q_1=\frac{2Q}{3}$
3. $Q_2=\frac{Q}{4},Q=\frac{3Q}{4}$
4. $Q_1=\frac{Q}{2},Q_2=\frac{Q}{2}$

Q. A charge Q is divided into two parts q and Q - q and separated by a distance R. The force of repulsion between them will be maximum when

1. $q=Q/2$
2. $q=Q/4$
3. $q=Q$
4. none of the above

Q.

Two-point charges A and B, having charges +Q and -Q respectively, are placed at a certain distance apart and the force acting between them is F. If 25% charge of A is transferred to B, then the force between the charges becomes

1. $\frac{16F}{9}$

2. $\frac{9F}{16}$

3. $\frac{4F}{3}$

4. F

Q.

Three charges $+q,+q$ and $+q$ are placed at the corners of an equilateral triangle of side 'a'. The resultant electric force on a charge $+q$ placed at the centre of the triangle is :

1. $\frac{1}{4\pi {ϵ}_0}.\frac{3Q^2}{a^2}$
2. $\frac{1}{4\pi {ϵ}_0}.\frac{3Q^2}{a}$
3. $\frac{1}{4\pi {ϵ}_0}.\frac{3\sqrt{3}{Q}^2}{a^2}$
4. $Zero$

Q. A total change Q is broken in two parts $Q_1$ and $Q_2$ and they are placed at a distance R from each other. The maximum force of repulsion between them will occur, when

Q.

What are the dimensions of K (coulomb’s law constant)?

1. Nm²/C²

2. NC²/m²

3. Nm²/C²

4. NC²/m²

Q. Two point charges $A$ and $B$ having charges $+Q$ and $-Q$ respectively are placed at certain distance apart and force acting between them is $F$. If $25$% charge of $A$ is transferred to $B$, then force between the charges becomes

1. $\frac{16F}{9}$
2. $\frac{4F}{3}$
3. $\frac{9F}{16}$
4. $F$

Q. The mechanical force acting per unit area of a charged conductor is :

1. $\frac{1}{2}{k\epsilon }_{\circ }{E}^2$
2. $\frac{a^2}{{2k\epsilon }_{\circ }}$
3. $\frac{1}{2}{k\epsilon }_{\circ }E$
4. both a and b

Q. Two point charges $100\mu \text{C}$ and $5\mu \text{C}$ are placed at points $\text{A}$ and $\text{B}$ respectively with $AB=40\text{cm}$.The workdone by external force in displacing the charge $5\mu \text{C}$ from $\text{B}$ to $\text{C}$ is
$\text{Here}BC=30\text{cm},$ $\angle ABC=\frac{\pi }{2}$

1. $\frac{81}{20}\text{J}$
2. $\frac{-9}{25}\text{J}$
3. $\frac{-9}{4}\text{J}$
4. $9\text{J}$

Q. Two identical particles are charged and held at a distance of $1m$ from each other. They are found to be attracting each other with a force of $0.027N$. Now, they are connected by a conducting wire so that charge flows between them. When the charge flow stops, they are found to be repelling each other with a force of $0.009N$. Find the initial charge on each particle :

1. None of these
2. $q_1=\pm 3\mu C;q_2=\mp 1\mu C$
3. $q_1=\mp 3\mu C;q_2=\mp 2\mu C$
4. $q_1=\pm 5\mu C;q_2=\mp 2\mu C$

Q. What must be the distance between point charge $q_1=26.0\mu C$ and point charge $q_2=47.0\mu C$ for the electrostatic force between them to have a magnitude of $5.70N$?

Q. An electron of mass $m$, charge $e$ falls through a distance $h$ meter in a uniform electric field $E$.

1. $t=\frac{2eE}{hm}$
2. $t=\frac{2hm}{eE}$
3. $t=\sqrt{\frac{2hm}{eE}}$
4. $t=\sqrt{\frac{2eE}{hm}}$

Q.

A charged particle of mass $5\times {10}^{-6}$ kg is held stationary in space by placing it in an electric field of strength ${10}^{6}N/C$ directed vertically downwards. The charge on the particle is: $(g=10m/s^2)$

1. $-20\times {10}^{-5}\mu C$
2. $-5\times {10}^{-5}\mu C$
3. $20\times {10}^{-5}\mu C$
4. $5\times {10}^{-5}\mu C$

Q. If $E,m,J$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Then the dimensions of $\frac{{EJ}^2}{m^5{G}^2}$ are same as that of

1. length
2. angle
3. mass
4. time

Q. Obtain the formula for electrostatic force and electric pressure on the surface of the charged conductor.

Q.

What are the dimensions of K (coulomb’s law constant)?

1. $\frac{N{m}^2}{C^2}$

2. $\frac{N{C}^2}{m^2}$

3. $\frac{Nm}{C^2}$

4. $\frac{NC}{m^2}$

Q. The closest numerical value to the ratio of permittivity of vaccum and gravitqtional constant is

1. ${10}^{-2}$
2. ${10}^{-1}$
3. ${10}^{-3}$
4. ${10}^{-4}$

Q. A charged particle $(Q={10}^{-4}C)$ is released from rest at $z=0$ in magnetic field given as $\overrightarrow{B}=B_0\cos (\omega t-kz)\hat{i}+B_1\cos (\omega t+kz)\hat{j}$ where $B_0=3\times {10}^{-5}T$ and $B_1=2\times {10}^{-6}T$. Then the rms value of force acting on particle is?

1. $3\times {10}^{-2}$
2. $0.6$
3. $0.9$
4. $0.1$

Q. The velocity of a body is expressed as $V=G^a{M}^b{R}^c$ where $G$ is gravitational constant, $M$ is mass and $R$ is the radius. The values of exponents $a,b$ and $c$ are:

1. $\frac{1}{2},\frac{1}{2},-\frac{1}{2}$
2. $1,1,1$
3. $\frac{1}{2},\frac{1}{2},\frac{1}{2}$
4. $1,1,\frac{1}{2}$

Q. In S = a + bt + $c{t}^2$. S is measured in metres and t in seconds. The unit of c is

1. No dimensions
2. m
3. $m{s}^{-1}$
4. $m{s}^{-2}$

Q. Two planets A and B have their radii in the ratio 2:52:5 respectively

1. The ratio of the acceleration due to gravity on them is $1:15$
2. For the same volume of planets, mass of planet A is greater than that of planet B
3. A body weighs $15$ times more on planet B than on planet A
4. Planet B has greater volume than planet A

Q. Two identical conducting spheres B and C are equally charged and there is a force of repulsion F between them when they are placed at some distance. The third spherical conductor is also identical to them but is uncharged. It is first kept in contact with B and then with C and is then separated. Determine the new force of repulsion between B and C.

Q. If the force between two charged objects separated by a distance d is to be left unchanged even though the charge on one of the objects is halved, keeping other the same, the new distance of separation becomes :

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