Angular momentum L = r × p. Position r has [L], linear momentum p = mv has [MLT⁻¹], so L has [L][MLT⁻¹] = [ML²T⁻¹]. This matches Planck's constant dimensions. Option A is linear momentum; C is energy/torque; D is dimensionless. Memory aid: 'Angular momentum: [ML²T⁻¹]; same as action quantities'. This dimensional analysis question tests ability to derive formulas, crucial for competitive exams. Always break down compound quantities into fundamental dimensions (M, L, T) for verification and problem-solving.
Explanation:
Lactometer is a specialized hydrometer for measuring milk purity/density. It works on Archimedes' principle: pure milk has specific density; adulteration (with water) changes density, altering lactometer reading. While it measures density, its specific application is milk testing. Option B is partially correct but not specific; competitive exams expect the precise application. Memory tip: 'Lacto = milk; meter = measure'. This application-based question tests knowledge of scientific instruments in daily life, frequently appearing in competitive exams. Always note context-specific uses of general instruments.
Explanation:
Work done by a variable force is the definite integral of F dx. W = Integral(3x^2 + 2x) dx from 1 to 2. W = [x^3 + x^2] evaluated from 1 to 2. Upper limit: (2^3 + 2^2) = 8 + 4 = 12. Lower limit: (1^3 + 1^2) = 1 + 1 = 2. Work = 12 - 2 = 10 Joules.
Explanation:
Electromagnetic waves are transverse: electric field (E) and magnetic field (B) are perpendicular to each other and both perpendicular to the direction of wave propagation. This is a fundamental property derived from Maxwell's equations. Memory tip: 'EM waves: E ⊥ B ⊥ propagation direction; right-hand rule for orientation'. This conceptual question tests electromagnetic wave fundamentals, crucial for modern physics in competitive exams. Always recall that EM waves require no medium and travel at speed of light in vacuum.
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