There is a uniform spherically symmetric surface charge density at a distance $R_0$ from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed $V(R(t))$ of the distribution as a function of its instantaneous radius $R(t)$ is
JEE MAIN 2019, Diffcult
Download our app for free and get startedPlay store
$U_{i}+K_{i}=U_{t}+K_{t}$

$\frac{\mathrm{k} \mathrm{Q}^{2}}{2 \mathrm{R}_{0}}+\mathrm{O}=\frac{\mathrm{k} \mathrm{Q}^{2}}{2 \mathrm{R}}+\frac{1}{2} \mathrm{mv}^{2}$

$V=\sqrt{\frac{k Q^{2}}{m}\left(\frac{1}{R_{0}}-\frac{1}{R}\right)}$

art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    Two capacitors connected in parallel having the capacities ${C_1}$ and ${C_2}$ are given $'q'$ charge, which is distributed among them. The ratio of the charge on ${C_1}$ and ${C_2}$ will be
    View Solution
  • 2
    Four metal conductors having different shapes

    $1.$  A sphere     $2.$  Cylindrical

    $3.$  Pear            $4.$  Lightning conductor

    are mounted on insulating stands and charged. The one which is best suited to retain the charges for a longer time is

    View Solution
  • 3
    Figure shows a solid metal sphere of radius $‘a’$ surrounded by a concentric thin metal shell of radius $2a$ . Initially both are having charges $Q$ each. When the two are connected by a conducting wire as shown in the figure, then amount of heat produced in this process will be 
    View Solution
  • 4
    The plates of a parallel plate capacitor are charged up to $100\, volt$. A $2\, mm$ thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\, mm$. The dielectric constant of the plate is
    View Solution
  • 5
    Two thin conducting shells of radii $R$ and $3R$ are shown in the figure. The outer shell carries a charge $+ Q$ and the inner shell is neutral. The inner shell is earthed with the help of a switch $S$.
    View Solution
  • 6
    Consider the shown system of two concentric thin metal shells. The inner hell has charge $Q$, while the outer shell is neutral. Potential difference between the shells is $V$. If the shell are joined by metal wire, then potential of the inner shell is
    View Solution
  • 7
    The capacity of a condenser is $4 \times {10^{ - 6}}$ farad and its potential is $100\,\,volts$. The energy released on discharging it fully will be.......$Joule$
    View Solution
  • 8
    Two condensers ${C_1}$and ${C_2}$ in a circuit are joined as shown in figure. The potential of point $A$ is ${V_1}$ and that of $B$ is ${V_2}$. The potential of point $D$ will be
    View Solution
  • 9
    A solid conducting sphere having a charge $Q$ is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now given a charge of $-3Q$, the new potential difference between the same two surfaces is......$V$
    View Solution
  • 10
    During charging a capacitor variation of potential $V$ of the capacitor with time $t$ is shown as
    View Solution