JEE Mains · Physics · STD 12 - Electric charges and fields
- JEE Mains 2024
- Hard
- MCQ
Two identical conducting spheres \(\mathrm{P}\) and \(\mathrm{S}\) with charge \(Q\) on each, repel each other with a force \(16 \mathrm{~N}\). A third identical uncharged conducting sphere \(\mathrm{R}\) is successively brought in contact with the two spheres. The new force of repulsion between \(\mathrm{P}\) and \(\mathrm{S}\) is what?
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(6 \mathrm{~N}\)
Step-by-step Solution
Detailed explanation
\(F_{P S} \propto Q^2\)
\(F_{P S}=16 N\)
Now If \(\mathrm{P} \& \mathrm{R}\) are brought in contact then
Now If \(\mathrm{S} \& \mathrm{R}\) are brought in contact then
New force between \(P \& S\) is :
\(\mathrm{F}_{\mathrm{PS}} \propto \frac{\mathrm{Q}}{2} \times \frac{3 \mathrm{Q}}{4}\)
\(\mathrm{~F}_{\mathrm{PS}} \propto \frac{3 \mathrm{Q}^2}{8}=\frac{3}{8} \times 16=6\)
\(F_{P S}=16 N\)
Now If \(\mathrm{P} \& \mathrm{R}\) are brought in contact then
Now If \(\mathrm{S} \& \mathrm{R}\) are brought in contact then
New force between \(P \& S\) is :
\(\mathrm{F}_{\mathrm{PS}} \propto \frac{\mathrm{Q}}{2} \times \frac{3 \mathrm{Q}}{4}\)
\(\mathrm{~F}_{\mathrm{PS}} \propto \frac{3 \mathrm{Q}^2}{8}=\frac{3}{8} \times 16=6\)
More questions from Physics
- M and R be the mass and radius of a disc. A small disc of radius \(R / 3\) is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis AB passing through the centre O and perpendicular to the plane of disc is \(\frac{4}{x} M R^2\). The value of \(x\) is ________.
JEE Mains 2025 Hard - A lift of mass \(1600\) kg is supported by thick iron wire. If the maximum stress which the wire can withstand is \(4 \times 10^8\) N/m\(^2\) and its radius is \(4\) mm, then maximum acceleration the lift can take is _______ m/s\(^2\). (take \(g = 10\) m/s\(^2\) and \(\pi = 3.14\))JEE Mains 2026 Medium
- In an experiment to determine the period of a simple pendulum of length \(1\, m\), it is attached to different spherical bobs of radii \(r_1\) and \(r_2\) . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be \(5\times10^{-4}\, s\), the difference in radii, \(\left| {{r_1} - {r_2}} \right|\) is best given by .... \(cm\)JEE Mains 2017 Hard
- In a closed organ pipe, the frequency of fundamental note is \(30 \mathrm{~Hz}\). A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to \(110 \mathrm{~Hz}\). If the organ pipe has a cross-sectional area of \(2 \mathrm{~cm}^2\), the amount of water poured in the organ tube is _______ \(g.\) (Take speed of sound in air is \(330 \mathrm{~m} / \mathrm{s}\) )JEE Mains 2024 Medium
- A spring whose unstretched length is \(\ell \) has a force constant \(k\). The spring is cut into two pieces of unstretched lengths \(\ell_1\) and \(\ell_2\) where, \(\ell_1 = n\ell_2\) and \(n\) is an integer. The ratio \(k_1/k_2\) of the corresponding force constants, \(k_1\) and \(k_2\) will beJEE Mains 2019 Medium
- In the following circuit, the battery has an emf of \(2\mathrm{V}\) and an internal resistance of \(\frac{2}{3}\ \Omega\). The power consumption in the entire circuit is _______ \(W\).
JEE Mains 2024 Hard
More PYQs from JEE Mains
- \(50\, W/m^2\) energy density of sunlight is normally incident on the surface of a solar panel. Some part of incident energy \((25\%)\) is reflected from the surface and the rest is absorbed. The force exerted on \(1\, m^2\) surface area will be close to \((c = 3 \times10^8\, m / s)\)JEE Mains 2019 Hard
- A 4 kg mass moves under the influence of a force \(\vec{F}=\left(4 t^3 \hat{i}-3 t \hat{j}\right) N\) where \(t\) is the time in second. If mass starts from origin at \(t=0\), the velocity and position after \(t=2 s\) will be :JEE Mains 2026 Medium
- A bullet of mass \(20\,g\) has an initial speed of \(1\,ms^{-1}\) just before it starts penetrating a mud wall of thickness \(20\,cm.\) If the wall offers a mean resistances of \(2.5 \times 10^{-2}\,N,\) the speed of the bullet after emerging from the other side of the wall is close to .............. \(\mathrm{ms}^{-1}\)JEE Mains 2019 Medium
- A particle of charge \(1.6 \mu \mathrm{C}\) and mass \(16 \mu \mathrm{~g}\) is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is ________ S. \((\pi=3.14)\)JEE Mains 2025 Easy
- A massless square loop, of wire of resistance \(10\,\Omega\). supporting a mass of \(1\,g\). hangs vertically with one of its sides in a uniform magnetic field of \(10^3\, G\), directed outwards in the shaded region. A dc voltage \(V\) is applied to the loop. For what value of V. the magnetic force will exactly balance the weight of the supporting mass of \(1\,g\) ? (If sides of the loop \(=10\,cm , g =10\,ms ^{-2}\) )
JEE Mains 2023 Medium