Two charged particles each having charge ' $q$ ' and mass ' $m$ ' are held at rest while their separation is ' $r$ '. The speed of the particles when their separation is ' $\frac{\mathrm{r}}{2}$ ' will be ( $\varepsilon_0=$ permittivity of the medium)

The pressure inside a soap bubble $A$ is 1.01 atmosphere and that in a soap bubble B is 1.02 atmosphere. The ratio of volume of bubble A to that of B is [Surrounding pressure $=1$ atmosphere]

In Young's double slit experiment, in an interference pattern, second minimum is observed exactly in front of one slit. The distance between the two coherent sources is ' $d$ ' and the distance between the source and screen is ' $D$ '. The wave length of light $(\lambda)$ used is

An observer moves towards a stationary source of sound with a velocity of one-fifth of the velocity of sound. The percentage increase in the apparent frequency is