Six point charges are kept $60^{\circ}$ apart from each other on the circumference of a circle of radius $R$ as shown in figure. The net electric field at the center of the circle is $\_\_\_\_$ .

( $\epsilon_0$ is permittivity of free space)

$7.9 \mathrm{MeV} \alpha$-particle scatters from a target material of atomic number 79 . From the given data the estimated diameter of nuclei of the target material is (approximately) $\_\_\_\_$ m.

$$ \left[\frac{1}{4 \pi \epsilon_{\mathrm{o}}}=9 \times 10^9 \mathrm{Nm}^2 / \mathrm{C}^2 \text { and electron charge }=1.6 \times 10^{-19} \mathrm{C}\right] $$

Net gravitational force at the center of a square is found to be $F_1$ when four particles having mass $M, 2 M, 3 M$ and $4 M$ are placed at the four corners of the square as shown in figure and it is $F_2$ when the positions of $3 M$ and $4 M$ are interchanged. The ratio $\frac{F_1}{F_2}$ is $\frac{\alpha}{\sqrt{5}}$. The value of $\alpha$ is $\_\_\_\_$ .

A meter bridge with two resistances $R_1$ and $R_2$ as shown in figure was balanced (null point) at 40 cm from the point $P$. The null point changed to 50 cm from the point $P$, when $16 \Omega$ resistance is connected in parallel to $R_2$. The values of resistances $R_1$ and $R_2$ are $\_\_\_\_$ .