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

If some charge is given to a solid metallic sphere, the field inside remains zero and by Gauss's law, all the charge resides on the surface. Suppose now that Coulomb's force between two charges varies as $\frac{1}{r^2}$, then for a charged solid metallic sphere,

A positive charge $q$ is placed at the centre of a neutral hollow cylindrical conducting shell with its cross-section as shown in the figure below:

Which one of the following figures correctly indicates the induced charge distribution on the conductor (ignore edge effects)?

A thin metallic disc is rotating with constant angular velocity about a vertical axis that is perpendicular to its plane and passes through its centre. The rotation causes the free electrons in the disc to redistribute. Assume that there is no external electric or magnetic field. Then,

An electrostatic field line leaves at an angle $\alpha$ from a point charge $q_1$ and connects with point charge $-q_2$ at an angle $\beta$ ($q_1$ and $q_2$ are positive) (see figure below). If $q_2=\frac{3}{2}{q}_1$ and $\alpha =30°$, then,

The potential due to an electrostatic charge distribution is, $V\left(r\right)=\frac{q{e}^{-\alpha r}}{4\pi {\epsilon }_{0}r}$ where, $\alpha$ is positive. The net charge within a sphere centred at the origin and of radius $\frac{1}{\alpha }$ is,

Two mutually perpendicular infinitely long straight conductors carrying uniformly distributed charges of linear densities ${\lambda }_1$ and ${\lambda }_2$ are positioned at a distance $r$ from each other.

The force between the conductors depends on $r$ as,