Which famous physicist correctly formulated the laws of electromagnetic induction mathematically, later synthesizing all known electromagnetic phenomena into four fundamental equations? MCQ with Answer and Explanation
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Question #1
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The universal law of gravitation states that the force between two masses is directly proportional to:
Correct Answer: Option C
Explanation:
Newton's law of gravitation: F = G·m₁m₂/r². Thus force is directly proportional to the product of the masses (m₁m₂) and inversely proportional to square of distance (r²). Option D incorrectly states 'directly proportional to square of distance' – it's inverse square. This fundamental law governs celestial mechanics. Memory tip: 'F ∝ m₁m₂ and F ∝ 1/r²'. Competitive exams often test precise wording of physical laws; distractors may reverse proportionality or misstate dependencies. Always recall the exact mathematical form.
Newton's law of gravitation: F = G·m₁m₂/r². Thus force is directly proportional to the product of the masses (m₁m₂) and inversely proportional to square of distance (r²). Option D incorrectly states 'directly proportional to square of distance' – it's inverse square. This fundamental law governs celestial mechanics. Memory tip: 'F ∝ m₁m₂ and F ∝ 1/r²'. Competitive exams often test precise wording of physical laws; distractors may reverse proportionality or misstate dependencies. Always recall the exact mathematical form.
Question #2
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A spring stores 18 J energy when stretched 3 cm. Force constant k is:
Correct Answer: Option D
Explanation:
Elastic PE: U = ½kx² ⇒ k = 2U/x². x = 3 cm = 0.03 m. k = 2×18/(0.03)² = 36/0.0009 = 40000 N/m. Unit conversion critical: cm to m. Memory aid: 'k = 2U/x²; always use SI units'. Tests spring energy formula application with unit conversion, frequently appearing in competitive exams.
Elastic PE: U = ½kx² ⇒ k = 2U/x². x = 3 cm = 0.03 m. k = 2×18/(0.03)² = 36/0.0009 = 40000 N/m. Unit conversion critical: cm to m. Memory aid: 'k = 2U/x²; always use SI units'. Tests spring energy formula application with unit conversion, frequently appearing in competitive exams.
Question #3
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Doppler effect for sound depends on:
Correct Answer: Option A
Explanation:
Apparent frequency change depends on relative velocity between source and observer with respect to medium. Both motions contribute: f' = f(v±v_o)/(v∓v_s). Memory tip: 'Approaching ⇒ higher pitch; receding ⇒ lower pitch'. Conceptual question testing Doppler effect fundamentals, frequently examined in competitive exams.
Apparent frequency change depends on relative velocity between source and observer with respect to medium. Both motions contribute: f' = f(v±v_o)/(v∓v_s). Memory tip: 'Approaching ⇒ higher pitch; receding ⇒ lower pitch'. Conceptual question testing Doppler effect fundamentals, frequently examined in competitive exams.
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