In space of horizontal $EF$ ($E = (mg)/q$) exist as shown in figure and a mass $m$ attached at the end of a light rod. If mass $m$ is released from the position shown in figure find the angular velocity of the rod when it passes through the bottom most position
$\sqrt {\frac{g}{l}} $
$\sqrt {\frac{{2g}}{l}} $
$\sqrt {\frac{{3g}}{l}} $
$\sqrt {\frac{{5g}}{l}} $
This question contains Statement$-1$ and Statement$-2$. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement$-1$ : For a charged particle moving from point $P$ to point $Q$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$.
Statement$-2$ : The net work done by a conservative force on an object moving along a closed loop is zero.
How much kinetic energy will be gained by an $\alpha - $particle in going from a point at $70\,V$ to another point at $50\,V$
If $3$ charges are placed at the vertices of equilateral triangle of charge ‘$q$’ each. What is the net potential energy, if the side of equilateral triangle is $l\, cm$
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).
A particle of mass $m$ and charge $q$ is placed at rest in a uniform electric field $E$ and then released. The kinetic energy attained by the particle after moving a distance $y$ is