Dielectrics Questions

A parallel plate capacitor with air between the plates has a capacitance of $9\text{pF}$. The separation between its plates is ‘$d$ ’. The space between the plates is now filled with two dielectrics. One has $k_1=3$ and thickness $d/3$ while the other has $k_2=6$ and thickness $2d/3$. Capacitance of the capacitor is now:

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ }$ with each other. When suspended in a liquid of density $0.8{\text{g cm}}^{-3}$, the angle remains the same. If density of the material of the sphere is $16{\text{g cm}}^{-3}$, the dielectric constant of the liquid is: