Escape velocity v_e = √(2GM/R), where M is planet mass, R its radius. Thus v_e depends on both M and R. It is independent of the escaping body's mass (as gravitational and inertial mass cancel). Memory tip: 'v_e ∝ √(M/R); larger M or smaller R ⇒ higher escape velocity'. This gravitation formula application is frequently tested in competitive exams. Always recall that escape velocity is a property of the planet, not the projectile. This problem assesses understanding of gravitational potential energy concepts.
Explanation:
Photoelectric equation: work function φ = hν₀, where ν₀ is threshold frequency. Thus ν₀ = φ/h = 2.3 eV / (4.14×10⁻¹⁵ eV·s) ≈ 5.555×10¹⁴ Hz ≈ 5.6×10¹⁴ Hz. This direct application tests photoelectric effect fundamentals. Memory aid: 'ν₀ = φ/h; higher work function ⇒ higher threshold frequency'. Competitive exams frequently provide h in eV·s for such calculations. Always ensure units match: eV for φ and h to avoid conversion errors. This problem assesses numerical proficiency in modern physics applications.
Explanation:
Doppler effect: apparent change in frequency due to relative motion. Siren pitch changes as it approaches/recedes. Echo is reflection. Bending is diffraction. Fusion is nuclear reaction.
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