Two point charges $+10 \mu \mathrm{C}$ and $4 \mu \mathrm{C}$ are placed 10 cm apart in air. The work required to be done to bring them 2 cm closer is

$$ \left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text { SI units }\right) $$

An inextensible string of length ' $l$ ' fixed at one end, carries a mass ' $m$ ' at the other end. If the string makes $\frac{1}{\pi}$ revolutions per second around the vertical axis through the fixed end, the tension in the string is [The string makes an angle $\theta$ with the vertical]

A coil of n turns and resistance $\mathrm{R} \Omega$ is connected in series with resistance $R / 4$. The combination is moved for time $t$ second through magnetic flux $\phi$ to $\phi_2$. The induced current in the circuit is

The gravitational pull of the moon is $\left(\frac{1}{6}\right)^{th}$ of the earth and mass of moon is $\left(\frac{1}{8}\right)^{\text {th }}$ of the earth. This implies that the