When a particle with charge \(+q\) is thrown with an initial velocity \(v\) towards another stationary change \(+Q,\) it is repelled back after reaching the nearest distance \(r\) from \(+Q.\) The closest distance that it can reach if it is thrown with an initial velocity \(2v,\) is:
1. | \(\frac{r}{4}\) | 2. | \(\frac{r}{2}\) |
3. | \(\frac{r}{16}\) | 4. | \(\frac{r}{8}\) |
1. | \(2C\) | 2. | \(\frac{C}{2}\) |
3. | \(4C\) | 4. | \(\frac{C}{4}\) |
1. | \(10 ~\mu \text{F}, ~6~\mu \text{F}\) | 2. | \(8 ~\mu \text{F}, ~8~\mu \text{F}\) |
3. | \(12~\mu \text{F},~ 4~\mu \text{F}\) | 4. | \(1.2~\mu \text{F},~1.8~\mu \text{F}\) |
Three capacitors, each of capacitance \(0.3~\mu \text{F}\) are connected in parallel. This combination is connected with another capacitor of capacitance \(0.1~\mu \text{F}\) in series. Then the equivalent capacitance of the combination is:
1. | \(0.9~\mu\text{F}\) | 2. | \(0.09~\mu\text{F}\) |
3. | \(0.1~\mu\text{F}\) | 4. | \(0.01~\mu\text{F}\) |
A hollow metal sphere of radius \(R\) is given \(+Q\) charges to its outer surface. The electric potential at a distance \(\frac{R}{3}\) from the centre of the sphere will be:
1. \(\frac{1}{4\pi \varepsilon_0}\frac{Q}{9R}\)
2. \(\frac{3}{4\pi \varepsilon_0}\frac{Q}{R}\)
3. \(\frac{1}{4\pi \varepsilon_0}\frac{Q}{3R}\)
4. \(\frac{1}{4\pi \varepsilon_0}\frac{Q}{R}\)
1. | \(1.5\times 10^{-6}~\text{J}\) | 2. | \(4.5\times 10^{-6}~\text{J}\) |
3. | \(3.25\times 10^{-6}~\text{J}\) | 4. | \(2.25\times 10^{-6}~\text{J}\) |
1. | dependent on the material property of the sphere |
2. | more on bigger sphere |
3. | more on smaller sphere |
4. | equal on both the spheres |
1. | \(9~{\mu \text{F}}\) | 2. | \(2~{\mu \text{F}}\) |
3. | \(3~{\mu \text{F}}\) | 4. | \(6~{\mu \text{F}}\) |