If an $\mathrm{\alpha }$-particle and a proton are accelerated from rest by a potential difference of 1 megavolt, then the ratio of their kinetic energies will be:

1. $\frac{1}{2}$

2. 1

3. 2

4. 4

Three charges -q, Q and -q are placed respectively at equal distances on a straight line. If the potential energy of the system of three charges is zero, then what is the ratio of Q:q?

1. 1: 1

2. 1: 2

3. 1: 3

4. 1: 4

A particle A has charge +q and another particle B has charge +4q with each of them having the same mass m. When allowed to fall from rest through the same electric potential difference, the ratio of their speeds $\frac{{\mathrm{v}}_{\mathrm{A}}}{{\mathrm{v}}_{\mathrm{B}}}$ will become:

1. 1: 2

2. 2: 1

3. 1: 4

4. 4: 1

If \(50~\text{J}\) of work must be done to move an electric charge of \(2~\text{C}\) from a point where the potential is \(-10~\text {volts}\) to another point where the potential is \(\text{V volts}\), then the value of \(\mathrm{V}\) is:
1. \(5~\text {volts}\)
2. \(-15~\text {volts}\)
3. \(+15~\text {volts}\)
4. \(+10~\text {volts}\)

A proton has a mass $1.67\times {10}^{-27}$ kg and a charge $+1.6\times {10}^{-19}$ C. If the proton is accelerated through a potential difference of 1 million volts, then the kinetic energy is:

1. $1.6\times {10}^{-15} \mathrm{J}$

2. $1.6\times {10}^{-13} \mathrm{J}$

3. $1.6\times {10}^{-21} \mathrm{J}$

4. $3.2\times {10}^{-13} \mathrm{J}$

Calculate the work done in taking a charge $-2\times {10}^{-9}$ C from A to B via C. (in the diagram)

1. 0.2 joule

2. 1.2 joule

3. 2.2 joule

4. Zero

Two electrons are moving towards each other, each with a velocity of ${10}^6$ m/s. What will be the closest distance of approach between them?

1. $1.53\times {10}^{-8} \mathrm{m}$

2. $2.53\times {10}^{-10} \mathrm{m}$

3. $3.53\times {10}^{-6} \mathrm{m}$

4. Zero

A point charge q is surrounded by eight identical charges at distance r as shown in the figure. How much work is done by the forces of electrostatic repulsion when the point charge at the centre is removed to infinity?

1. Zero

2. $\frac{8{\mathrm{q}}^2}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}$

3. $\frac{8\mathrm{q}}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}$

4. $\frac{64{\mathrm{q}}^2}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}$

1000 small water drops, each of capacitance C, join together to form one large spherical drop. The capacitance of the bigger sphere is:

1. C

2. 10C

3. 100C

4. 1000C

Two similar conducting balls having charges +q and -q are placed at a separation d from each other in the air. The radius of each ball is r and the separation between their centres is d(d>>r). Calculate the capacitance of the two-ball system.

1. $4{\mathrm{\pi \epsilon }}_0\mathrm{r}$

2. $2{\mathrm{\pi \epsilon }}_0\mathrm{r}$

3. $4{\mathrm{\pi log}}_{\mathrm{e}}\frac{{\mathrm{\epsilon }}_0\mathrm{r}}{\mathrm{d}}$

4. $4{\mathrm{\pi log}}_{\mathrm{e}}\frac{\mathrm{r}}{\mathrm{d}}$