Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5 \mathrm{~g} / \mathrm{cc}$, the dielectric constant of water will be

(Take density of water $=1 \mathrm{~g} / \mathrm{cc}$ )

  • A$4$
  • B$8$
  • C$7$
  • D$3$
JEE MAIN 2024, Diffcult
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
    The effective capacitance between the points $P$ and $Q$ of the arrangement shown in the figure is......$\mu F$
    View Solution
  • 2
    A parallel-plate capacitor of area $A,$ plate separation $d$ and capacitance $C$ is filled with four dielectric materials having dielectric constants $K_1,K_2,K_3$ and $K_4$ as shown in the figure. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $K$ is given by 
    View Solution
  • 3
    The equivalent capacitance between points $A$ and $B$ of the circuit shown will be
    View Solution
  • 4
    Three capacitors of capacitances $25 \mu \mathrm{F}, 30 \mu \mathrm{F}$ and $45 \mu \mathrm{F}$ are connected in parallel to a supply of $100$

    $V$. Energy stored in the above combination is $\mathrm{E}$. When these capacitors are connected in series to the same supply, the stored energy is $\frac{9}{\mathrm{x}} \mathrm{E}$. The value of $x$ is___________.

    View Solution
  • 5
    Two insulated charged spheres of radii $20\,cm$ and $25\,cm$ respectively and having an equal charge $Q$ are connected by a copper wire, then they are separated
    View Solution
  • 6
    The capacity of a parallel plate condenser is $10\,\mu F$ without dielectric. Dielectric of constant $2$ is used to fill half the distance between the plates, the new capacitance in $\mu F$ is
    View Solution
  • 7
    The value of electric potential at any point due to any electric dipole is
    View Solution
  • 8
    Four identical thin, square metal sheets, $S_1, S_2, S_3$, and $S_4$, each of side $a$ are kept parallel to each other with equal distance $d( < < a)$ between them, as shown in the figure. Let $C_0=\varepsilon_0 a^2 / d$, where $\varepsilon_0$ is the permittivity of free space.

    Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option.

    $List-I$ $List-II$
    ($P$) The capacitance between $S_1$ and $S_4$, with $S_2$ and $S_3$ not connected, is ($1$) $3 C_0$
    ($Q$) The capacitance between $S_1$ and $S_4$, with $S_2$ shorted to $S_3$, is ($2$) $C_0 / 2$
    ($R$) The capacitance between $S_1$ and $S_3$, with $S_2$ shorted to $S_4$, is ($3$) $C_0 / 3$
    ($S$) The capacitance between $S_1$ and $S_2$, with $S_3$ shorted to $S_1$, and $S_2$ shorted to $S_4$, is ($4$) $2 C_0 / 3$
      ($5$) $2 C_0$

    View Solution
  • 9
    Two Identical capacttors $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ of equal capacitance are connected as shown in the circult. Terminals $a$ and $b$ of the key $k$ are connected to charge capacitor $\mathrm{C}_{1}$ using battery of $emf \;V\; volt$. Now disconnecting $a$ and $b$ the terminals $b$ and $c$ are connected. Due to this, what will be the percentage loss of energy?.....$\%$
    View Solution
  • 10
    Figure given below shows two identical parallel plate capacitors connected to a battery with switch $S$ closed. The switch is now opened and the free space between the plate of capacitors is filled with a dielectric of dielectric constant $3$. What will be the ratio of total electrostatic energy stored in both capacitors before and after the introduction of the dielectric
    View Solution