Explanation:
Pendulum period T = 2π√(l/g) for small amplitudes. It depends on length l and gravity g, but not on bob mass or amplitude (isochronism for small angles). Mass independence arises because gravitational force and inertia both proportional to mass, canceling out. Memory aid: 'Pendulum: T ∝ √(l/g); independent of mass and small-amplitude'. This conceptual question tests oscillations fundamentals, frequently examined in competitive exams. Always verify the small-angle approximation; competitive exams assume it unless specified otherwise. This problem assesses understanding of which parameters affect periodic motion.
Explanation:
F = m×a. New force F' = (2m)×(a/2) = m×a = F. So force remains unchanged. This is direct proportionality. Understand the relationship: doubling mass doubles force, halving acceleration halves it, net effect no change.
Explanation:
Ideal solenoid interior has uniform magnetic field B = μ₀ n I, parallel to axis. Outside field weak. Used in electromagnets, relays. Uniformity for scientific instruments.
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