MHT CET · Physics · Electrostatics
' \(n\) ' small drops of same size are charged to 'V' volt each. If they coalesce to form a single large drop, then its potential will be
- A \(\mathrm{Vn}^{\frac{1}{3}}\)
- B \(\mathrm{Vn}^{\frac{2}{3}}\)
- C \(V \cdot n\)
- D \(\mathrm{Vn}^{-1}\)
Answer & Solution
Correct Answer
(B) \(\mathrm{Vn}^{\frac{2}{3}}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{V}=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q}}{\mathrm{r}}\)
\(\begin{aligned} \mathrm{V}^{\prime} & =\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q}^{\prime}}{\mathrm{r}^{\prime}} \\ & =\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{nq}}{\mathrm{n}^{1 / 3} \mathrm{r}} \quad\left(\because \mathrm{q}^{\prime}=\mathrm{nq}, \mathrm{r}^{\prime}=\mathrm{n}^{1 / 3} \mathrm{r}\right) \\ \mathrm{V}^{\prime} & =\mathrm{Vn}^{2 / 3}\end{aligned}\)
\(\begin{aligned} \mathrm{V}^{\prime} & =\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q}^{\prime}}{\mathrm{r}^{\prime}} \\ & =\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{nq}}{\mathrm{n}^{1 / 3} \mathrm{r}} \quad\left(\because \mathrm{q}^{\prime}=\mathrm{nq}, \mathrm{r}^{\prime}=\mathrm{n}^{1 / 3} \mathrm{r}\right) \\ \mathrm{V}^{\prime} & =\mathrm{Vn}^{2 / 3}\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- The relative permeability of iron is 2000 . Its absolute permeability in SI unit will be \(\left(\frac{\mu_0}{4 \pi}=10^{-7}\right.\) SI unit \()\)MHT CET 2021 Easy
- The bob of a simple pendulum performs SHM with period \(T\) in air and with period \(T_1\) in water. Relation between \(T\) and \(T_1\) is (neglect friction due to water, density of the material of the bob is \(\frac{9}{8} \times 10^3 kg / m ^3\), density of water is \(1 g / cc\) )MHT CET 2016 Medium
- Two identical wires are vibrating in unison. If the tension in one of the wires is
increased by \(2 \%\), five beats are produced per second by the two vibrating wires.
The initial frequency of each wire is \((\sqrt{1 \cdot 02} \doteq 1 \cdot 01)\)MHT CET 2020 Easy - Two light rays having the same wavelength ' \(\lambda\) ' in vacuum are in phase initially. Then, the first ray travels a path ' \(\mathrm{L}_1\) ' through a medium of refractive index ' \(\mu_1\) ' while the second ray travels a path of length ' \(\mathrm{L}_2\) ' through a medium of refractive index ' \(\mu_2\) '. The two waves are then combined to observe interference. The phase difference between the two waves isMHT CET 2024 Easy
- A molecule consists of two atoms each of mass ' \(\mathrm{m}\) ' and separated by a distance ' \(d\) '. At room temperature, if the average rotational kinetic energy is ' \(\mathrm{E}\) ' then the angular frequency isMHT CET 2021 Medium
- An air-filled parallel plate capacitor has a capacity \(2 \mathrm{pF}\), The separation of the plates is doubled and the interspace between the plates is filled with dielectric material, then the capacity is increased to \(6 \mathrm{pF}\), The dielectric constant of the material isMHT CET 2021 Medium
More PYQs from MHT CET
- In a triangle \(A B C\), with usual notations, if
\(\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}\) Then \(\cos A: \cos B: \cos C\) isMHT CET 2025 Medium - Identify the product \(X\) in the following reaction. Sodium propanoate \(\xrightarrow[\Delta]{\text { soda-lime }} X+\) sodium carbonateMHT CET 2024 Hard
- For a gas at a particular temperature on an average, the quantity which remains same for all molecules isMHT CET 2025 Easy
- The function \(x^5-5 x^4+5 x^3-10\) has a maximum, when \(x\) is equal toMHT CET 2025 Medium
- What is the bond order in \(\mathrm{N}_2^*\) ?MHT CET 2023 Easy
- Which of the following is NOT a characteristic of chemisorption?MHT CET 2022 Easy