The time period of a block of mass $m$ suspended from the upper plate of a parallel plate capacitor by a spring of stiffness $k$ is $T$ when the block is uncharged. If a charge $q$ is given to the block,what will be the new time period of oscillation?

$A$ unit positive point charge of mass $m$ is projected with a velocity $V$ inside a tunnel as shown. The tunnel is made inside a uniformly charged non-conducting sphere of radius $R$ and volume charge density $\rho$. The minimum velocity with which the point charge should be projected such that it can reach the opposite end of the tunnel is equal to

Two identical balls having like charges and placed at a certain distance apart repel each other with a certain force. They are brought in contact and then moved apart to a distance equal to half their initial separation. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls is

$A$ charge $Q$ is uniformly distributed over the volume of an insulating sphere of radius $R$. $A$ thin metal shell of radius $b$ $(b > R)$ with a charge $-Q$ is placed around the sphere. The space between the sphere and the shell is filled with air. Which of the following graphs correctly represents the electric field $E$ as a function of distance $r$ from the center?

$A$ solid sphere of radius $R$ carries a charge $(Q+q)$ distributed uniformly over its volume. $A$ very small point-like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge $q$. If it acquires a speed $v$ when it has fallen through a vertical height $y$ (see figure),then: (assume the remaining portion to be spherical).

Which of the following patterns of electric field lines is $NOT$ possible for an electrostatic field due to static charges?