The electric field intensity on the surface of a solid charged sphere of radius $\mathbf{r}$ and volume charge density $\sigma$ is ( $\varepsilon_0=$ permittivity of free space)

Two strings ' X ' and ' Y ' of a guitar produces a beat frequency of 6 Hz . When the tension of the string ' Y ' is increased, the beat frequency is found to be 4 Hz . If the frequency of string ' X ' is 300 Hz , then the original frequency of string ' Y ' is

In common emitter mode of a transistor, the current gain is 8 . The input impedance is $25 \mathrm{k} \Omega$ and load resistance is $75 \mathrm{k} \Omega$. The power gain is

A transverse displacement of vibrating string is $y=0.06 \sin \left(\frac{2 \pi}{3}\right) \times \cos (120 \pi t)$.

If the mass per unit length of a string is $4 \times 10^{-2} \mathrm{~kg} / \mathrm{m}$, then the tension in the string will be