A 2$$\mu$$F capacitor C₁ is first charged to a potential difference of 10V using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor C₂ of 8 $$\mu$$F. The charge in C₂ on equilibrium condition is ____________ $$\mu$$C. (Round off to the Nearest Integer)

A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is __________ N. (Round off to the Nearest Integer) [Take g = 10 ms^-2 ]

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction $${1 \over {\sqrt 3 }}$$. It is desired to make the body move by applying the minimum possible force F N. The value of F will be ____________. (Round off to the Nearest Integer) [Take g = 10 ms^$$-$$2 ]

A particle of mass m moves in a circular orbit in a
central potential field U(r) = U₀r⁴. If Bohr's quantization conditions
are applied, radii of possible
orbitals r_n vary with $${n^{{1 \over \alpha }}}$$, where $$\alpha$$ is ____________.