Embibe Experts Solutions for Chapter: Electrostatics, Exercise 2: Exercise 2

Two positively charged spheres of masses $m_1$ and $m_2$, are suspended from a common point at the ceiling by identical insulating massless strings of length $l$. Charges on the two spheres are $q_1$ and $q_2$, respectively. At equilibrium both strings make the same angle $\theta$ with the vertical. Then

Two equal charges of magnitude $Q$ each are placed at a distance $d$ apart. Their electrostatic energy is $E.A.$ third charge $-\frac{Q}{2}$ is brought midway between these two charges. The electrostatic energy of the system is now?

Two small metal balls of different mass $m_1$ and $m_2$ are connected by strings of equal length to a fixed point. When the balls are given charges, the angles that the two strings make with the vertical are $30°$ and $60°$, respectively. The ratio $\frac{m_1}{m_2}$, is close to

An electric field due to a positively charged long straight wire at a distance $r$ from it is proportional to $r^{-1}$ in magnitude. Two electrons are orbiting such a long straight wire in circular orbits of radii $1 \stackrel{\circ }{\mathrm{A}}$ and $2 \stackrel{\circ }{\mathrm{A}}$. The ratio of their respective time periods is

A $20 \mathrm{g}$ bullet whose specific heat is $5000 \mathrm{J} {\mathrm{kg}}^{-1}{}^{\circ }\mathrm{C}^{-1}$ and moving at $2000 \mathrm{m} {\mathrm{s}}^{-1}$ plunges into a $1.0 \mathrm{kg}$ block of wax whose specific heat is $3000 \mathrm{J} {\mathrm{kg}}^{-1}{}^{\circ }\mathrm{C}^{-1}$. Both bullet and wax are at $25 °\mathrm{C}$ and assume that $\left(\mathrm{i}\right)$ the bullet comes to rest in the wax and $\left(\mathrm{ii}\right)$ all its kinetic energy goes into heating the wax. Thermal temperature of the wax in ${}^{\circ }\mathrm{C}$ is close to.

Positive point charges are placed at the vertices of a star shape as shown in the figure.

Direction of the electrostatic force on a negative point charge at the centre $O$ of the star is

A total solar eclipse is observed from the earth. At the same time, an observer on the moon views the earth. She is most likely to see (E denotes the earth)

A proton of mass $m$ and charge $e$ is projected from a very large distance towards an $\alpha$ particle with velocity $v$. Intially, $\alpha$ particle is at rest, but it is free to move. If gravity is neglected, then the minimum separation along the straight line of their motion will be