JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance
\(512\) identical drops of mercury are charged to a potential of \(2\, V\) each. The drops are joined to form a single drop. The potential of this drop is ......... \(V.\)
- A \(128\)
- B \(256\)
- C \(64\)
- D \(144\)
Answer & Solution
Correct Answer
(A) \(128\)
Step-by-step Solution
Detailed explanation
\(Q =512 q\) Volume \(_{i}=\) Volume \(_{f}\) \(512 \times \frac{4}{3} \pi r^{3}=\frac{4}{3} \pi R^{3}\) \(2^{9} r ^{3}= R ^{3}\) \(R =8 r\) \(2=\frac{ kq }{ r }\) \(V =\frac{ kQ }{ R }=\frac{ k 512 q }{8 r }\) \(V =128\)
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
- An electric field \(\overrightarrow{\mathrm{E}}=(2 \mathrm{xi}) \mathrm{NC}^{-1}\) exists in space. \(\mathrm{A}\) cube of side \(2 \mathrm{~m}\) is placed in the space as per figure given below. The electric flux through the cube is _______ \(\mathrm{Nm}^2 / \mathrm{C}\)
JEE Mains 2024 Hard - The engine of a train moving with speed \(10\,ms ^{-1}\) towards a platform sounds a whistle at frequency \(400\,Hz\). The frequency heard by a passenger inside the train is \(........\,Hz\) (neglect air speed. Speed of sound in air \(330\,ms ^{-1}\) )JEE Mains 2023 Medium
- \(ABC\) is a plane lamina of the shape of an equilateral triagnle. \(D,\) \(E\) are mid points of \(AB\), \(AC\) and \(G\) is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through \(G\) and perpendicular to the plane \(ABC\) is \(I _{0} .\) If part \(ADE\) is removed, the moment of inertia of the remaining part about the same axis is \(\frac{ NI _{0}}{16}\) where \(N\) is an integer. Value of \(N\) is
JEE Mains 2020 Hard - A series combination of resistor of resistance \(100\,\Omega\), inductor of inductance \(1\,H\) and capacitor of capacitance \(6.25\,\mu F\) is connected to an ac source. The quality factor of the circuit will be \(.............\).JEE Mains 2023 Medium
- A \(60\; HP\) electric motor lifts an elevator having a maximum total load capacity of \(2000\; \mathrm{kg}\). If the frictional force on the elevator is \(4000 \;\mathrm{N}\). the speed of the elevator at full load is close to .............. \(\mathrm{m} / \mathrm{s}\) \(\left(1 \;\mathrm{HP}=746 \;\mathrm{W}, \mathrm{g}=10\; \mathrm{ms}^{-2}\right)\)JEE Mains 2020 Medium
- A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is __________ grams.
(Latent heat of fusion of lead \(=2.5 \times 10^4 \mathrm{JKg}^{-1}\) and specific heat capacity of lead \(=125 \mathrm{JKg}^{-1}\) \(\left.\mathrm{K}^{-1}\right)\)JEE Mains 2025 Medium
More PYQs from JEE Mains
- A balloon was moving upwards with a uniform velocity of \(10\, {m} / {s}\). An object of finite mass is dropped from the balloon when it was at a height of \(75\, {m}\) from the ground level. The height of the balloon from the ground when object strikes the ground was around.(In \({m}\)) (Takes the value of \(g\) as \(10 \,{m} / {s}^{2}\) )JEE Mains 2021 Hard
- If the function \(\mathrm{f}\) defined on \(\left(-\frac{1}{3}, \frac{1}{3}\right)\) by \(f(x)=\left\{\begin{array}{ll}{\frac{1}{x} \log _{e}\left(\frac{1+3 x}{1-2 x}\right)} & {, \text { when } x \neq 0} \\ {k} & {, \text { when } x=0}\end{array}\right.\) is continuous, then \(\mathrm{k}\) is equal toJEE Mains 2020 Hard
- If the \(rms\) speed of oxygen molecules at \(0^{\circ} {C}\) is \(160\; {m} / {s}\), find the rms speed of hydrogen molecules at \(0^{\circ} {C}\). (In \({m}/{s}\))JEE Mains 2021 Medium
- For some \(\theta\in(0,\frac{\pi}{2}),\) let the eccentricity and the length of the latus rectum of the hyperbola \(x^{2}-y^{2}sec^{2}\theta=8\) be \(e_{1}\) and \(l_{1}\), respectively, and let the eccentricity and the length of the latus rectum of the ellipse \(x^{2}sec^{2}\theta+y^{2}=6\) be \(e_{2}\) and \(l_{2},\) respectively. If \(e_{1}^{2}=e_{2}^{2}(sec^{2}\theta+1)\), then \((\frac{l_{1}l_{2}}{e_{1}e_{2}})tan^{2}\theta\) is equal to ___ .JEE Mains 2026 Medium
- The number of solutions of the equation \(2 x+3 \tan x=\pi, x \in[-2 \pi, 2 \pi]-\left\{ \pm \frac{\pi}{2}, \pm \frac{3 \pi}{2}\right\}\) isJEE Mains 2025 Easy
- A uniform wire (Young's modulus \(2 \times 10^{11}\, Nm^{-2}\) ) is subjected to longitudinal tensile stress of \(5 \times 10^7\,Nm^{-2}\) . If the over all volume change in the wire is \(0.02\%,\) the fractional decrease in the radius of the wire is close toJEE Mains 2013 Medium