JEE Mains · Physics · STD 12 - Electric potential and capacitance
- JEE Mains 2021
- Medium
- Numerical
A parallel plate capacitor whose capacitance \(C\) is \(14\, pF\) is charged by a battery to a potential difference \(V =12\, V\) between its plates. The charging battery is now disconnected and a porcelin plate with \(k =7\) is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of \(..........pJ\). (Assume no friction)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(864\)
Step-by-step Solution
Detailed explanation
\(U _{ i }=\frac{1}{2} \times 14 \times 12 \times 12 pJ \quad\left(\because U =\frac{1}{2} CV ^{2}\right)\)
\(=1008 pJ\)
\(U _{ f }=\frac{1008}{7} pJ =144 pJ \quad\left(\because C _{ m }= k C _{0}\right)\)
Mechanical energy \(=\Delta U\)
\(=1008-144\)
\(=864 pJ\)
More questions from Physics
- For the four sets of three measured physical quantities as given below. Which of the following options is correct ? \((i)\) \(\mathrm{A}_{1}=24.36, \mathrm{B}_{1}=0.0724, \mathrm{C}_{1}=256.2\) \((ii)\) \(\mathrm{A}_{2}=24.44, \mathrm{B}_{2}=16.082, \mathrm{C}_{2}=240.2\) \((iii)\) \(\mathrm{A}_{3}=25.2, \mathrm{B}_{3}=19.2812, \mathrm{C}_{3}=236.183\) \((iv)\) \(\mathrm{A}_{4}=25, \mathrm{B}_{4}=236.191, \mathrm{C}_{4}=19.5\)JEE Mains 2020 Hard
- A uniform heavy rod of mass \(20\,kg\). Cross sectional area \(0.4\,m ^{2}\) and length \(20\,m\) is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is \(x \times 10^{-9} m\). The value of \(x\) is (Given. Young's modulus \(Y =2 \times 10^{11} Nm ^{-2}\) અને \(\left.g=10\, ms ^{-2}\right)\)JEE Mains 2022 Hard
- A plane electromagnetic wave of wavelength \(\lambda \) has an intensity \(I.\) It is propagating along the positive \(Y-\) direction. The allowed expressions for the electric and magnetic fields are given byJEE Mains 2018 Medium
- The angular momentum for the electron in Bohr's orbit is \(L\). If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will beJEE Mains 2023 Medium
- Given below are two statements: \(Statement\) \(I\) : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water. \(Statement\) \(II\) : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water. In the light of the above statements, choose the most appropriate from the options given belowJEE Mains 2024 Hard
- Two satellites \(A\) and \(B\) having masses in the ratio \(4: 3\) are revolving in circular orbits of radii \(3\,r\) and \(4\,r\) respectively around the earth. The ratio of total mechanical energy of \(A\) to \(B\) is.JEE Mains 2022 Medium
More PYQs from JEE Mains
- The r.m.s speed of oxygen molecules at \(47^{\circ} C\) is equal to that of the hydrogen molecules kept at _________ \({ }^{\circ} C\). (Mass of oxygen molecule/mass of hydrogen molecule \(=32 / 2\) )JEE Mains 2026 Medium
- \(\sigma\) is the uniform surface charge density of a thin spherical shell of radius \(R\). The electric field at any point on the surface of the spherical shell is _______.JEE Mains 2024 Hard
- A hole is drilled in a metal sheet. At \(27^{\circ} C\), the diameter of hole is 5 cm . When the sheet is heated to \(177^{\circ} C\), the change in the diameter of hole is \(d \times 10^{-3} cm\). The value of \(d\) will be ________ , if coefficient of linear expansion of the metal is \(1.6 \times 10^{-5} /{ }^{\circ} C\)JEE Mains 2023 Medium
- A metal wire of uniform mass density having length \(L\) and mass \(M\) is bent to form a semicircular arc and a particle of mass \(m\) is placed at the centre of the arc. The gravitational force on the particle by the wire is _______.JEE Mains 2024 Hard
- A uniform rod of mass m and length \(l\) suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is _________.(g acceleration due to gravity)
JEE Mains 2026 Easy