Mirror focal length f and radius R relation: MCQ with Answer and Explanation

Explanation:
SHM definition: acceleration a ∝ -x (displacement), i.e., a = -ω²x. This restoring acceleration causes oscillatory motion. Constant acceleration implies uniformly accelerated motion (not oscillatory). Constant velocity implies no acceleration. Memory tip: 'SHM: a = -ω²x; force F = -kx (Hooke's law)'. This conceptual question tests fundamental SHM characteristics, frequently examined in competitive exams. Always link to examples: mass-spring system, simple pendulum (small angles), LC circuits.

Explanation:
Control rods (made of cadmium, boron, or hafnium) absorb neutrons to regulate the fission chain reaction rate. Inserting rods deeper reduces neutron population, slowing reaction; withdrawing them increases reaction rate. Moderators (water, graphite) slow neutrons to thermal energies for efficient fission. Memory aid: 'Control rods = neutron absorbers; Moderators = neutron slowers'. This application question tests knowledge of reactor components, common in competitive exams. Always distinguish roles: fuel (fissionable material), moderator, control rods, coolant.

Explanation:
By Ampere's Circuital Law, for a solid wire carrying uniform current, the magnetic field inside (r < R) is B = (mu_0 * I * r) / (2piR^2), meaning B ∝ r (straight line). Outside the wire (r > R), B = (mu_0 * I) / (2pi*r), meaning B ∝ 1/r (rectangular hyperbola). Thus, it increases linearly then decays.