A and B are two identical blocks made of a co | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) At equilibrium,the electrostatic repulsive force between the two blocks is balanced by the spring force.The electrostatic force between the two bl

Vedclass · Accepted Answer

$2L\sqrt {4\pi {\varepsilon _0}K\left( {L - {L_0}} \right)} $

Vedclass · Answer

(C) At equilibrium,the electrostatic repulsive force between the two blocks is balanced by the spring force.The electrostatic force between the two blocks,each having charge $Q/2$,separated by a distance $L$ is given by Coulomb's Law:$F_e = \frac{1}{4 \pi \varepsilon_{0}} \frac{(Q/2)(Q/2)}{L^2} = \frac{1}{4 \pi \varepsilon_{0}} \frac{Q^2}{4L^2}$The spring force for an extension $(L - L_0)$ is given by Hooke's Law:$F_s = K(L - L_0)$Equating the two forces at equilibrium:$\frac{1}{4 \pi \varepsilon_{0}} \frac{Q^2}{4L^2} = K(L - L_0)$Solving for $Q^2$:$Q^2 = 4L^2 \cdot 4 \pi \varepsilon_{0} K(L - L_0)$$Q^2 = 16 \pi \varepsilon_{0} K L^2 (L - L_0)$Taking the square root on both sides:$Q = 4L \sqrt{\pi \varepsilon_{0} K (L - L_0)}$Wait,let us re-evaluate the provided options. If we simplify the expression:$Q^2 = 4 \pi \varepsilon_0 K (2L)^2 (L - L_0) / 1$ is not matching. Let's re-check the algebra:$\frac{Q^2}{16 \pi \varepsilon_0 L^2} = K(L - L_0)$$Q^2 = 16 \pi \varepsilon_0 L^2 K (L - L_0)$$Q = 4L \sqrt{\pi \varepsilon_0 K (L - L_0)}$Looking at option $C$: $2L \sqrt{4 \pi \varepsilon_0 K (L - L_0)} = 2L \cdot 2 \sqrt{\pi \varepsilon_0 K (L - L_0)} = 4L \sqrt{\pi \varepsilon_0 K (L - L_0)}$.Thus,option $C$ is correct.

Similar Questions

Two identically charged pith balls are suspended from the same point by two massless identical threads. The density of each ball is $\rho$. If the system is immersed in a medium of density $\sigma$ and the balls remain at the same angle of deflection,then the dielectric constant of the medium is:

Two equal charges $q$ are placed at $x = -a$ and $x = a$ on the $x$-axis. $A$ particle of mass $m$ and charge $q_0 = q/2$ is placed at the origin. If the charge $q_0$ is given a small displacement $(y << a)$ along the $y$-axis,the net force acting on the particle is proportional to .......

The electrical force between two point charges is $200 \ N$. If we increase $10 \ \%$ charge on one of the charges and decrease $10 \ \%$ charge on the other,then the electrical force between them for the same distance becomes . . . . . . . . . . (in $N$)

Two charges are at a distance $d$ apart. If a copper plate (conducting medium) of thickness $d/2$ is placed between them,the effective force will be

Three equal charges are placed on the three corners of a square. If the force between $q_1$ and $q_2$ is $F_{12}$ and that between $q_1$ and $q_3$ is $F_{13}$,the ratio of magnitudes $\frac{F_{12}}{F_{13}}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module