Two identical positive charges $$Q$$ each are fixed at a distance of '2a' apart from each other. Another point charge $$q_{0}$$ with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $$\mathrm{q}_{0}$$ executes $$\mathrm{SHM}$$. The time period of oscillation of charge $$\mathrm{q}_{0}$$ will be :

Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The internal resistances of the two sources are $$r_{1}$$ and $$r_{2}$$ $$\left(r_{1}>r_{2}\right)$$. If the potential difference across the source of internal resistance $$r_{1}$$ is zero, then the value of R will be :

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of $$3 \mathrm{~s}$$ and $$4 \mathrm{~s}$$ respectively. If their moments of inertia are in the ratio of $$3: 2$$, then the ratio of their magnetic moments will be:

A magnet hung at $$45^{\circ}$$ with magnetic meridian makes an angle of $$60^{\circ}$$ with the horizontal. The actual value of the angle of dip is -