A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance between the centres of the two spheres is 5 m. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint?

Statement I :

Two forces $$\left( {\overrightarrow P + \overrightarrow Q } \right)$$ and $$\left( {\overrightarrow P - \overrightarrow Q } \right)$$ where $$\overrightarrow P \bot \overrightarrow Q $$, when act at an angle $$\theta$$₁ to each other, the magnitude of their resultant is $$\sqrt {3({P^2} + {Q^2})} $$, when they act at an angle $$\theta$$₂, the magnitude of their resultant becomes $$\sqrt {2({P^2} + {Q^2})} $$. This is possible only when $${\theta _1} < {\theta _2}$$.

Statement II :

In the situation given above.

$$\theta$$₁ = 60$$^\circ$$ and $$\theta$$₂ = 90$$^\circ$$

In the light of the above statements, choose the most appropriate answer from the options given below :-

A free electron of 2.6 eV energy collides with a H⁺ ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. (h = 6.6 $$\times$$ 10^$$-$$34 Js)

Two thin metallic spherical shells of radii r₁ and r₂ (r₁ < r₂) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature $$\theta$$₁ and the outer shell at temperature $$\theta$$₂($$\theta$$₁ < $$\theta$$₂). The rate at which heat flows radially through the material is :-