Two particles $$A$$ and $$B$$ having same mass have charge $$+q$$ and $$+4 q$$ respectively. When they are allowed to fall from rest through same electric potential difference, the ratio of their speeds '$$V_A$$' to '$$\mathrm{V}_{\mathrm{B}}$$' will become

When a piece of polythene is rubbed with wool, a negative charge of $$4 \times 10^{-7} \mathrm{C}$$ is developed on the polythene. The number of electrons transferred from wool to polythene is $$[e=1.6 \times\left.10^{-19} \mathrm{C}\right]$$

A hollow metal sphere has a radius 'r'. The potential difference between a point on its surface and at a point at a distance '3r' from its centre is 'V'. The electric intensity at the distance '3r' from the centre of the sphere will be :

'$$\mathrm{F}$$' is the force between the two identical charged particles placed at a distance '$$\mathrm{Y}$$' from each other. If the distance between the charges is reduced to half the previous distance then force between them becomes