Pendulum T measured 2.0±0.1 s. % error in g: MCQ with Answer and Explanation
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Question #1
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The dimensional formula for energy density (energy per unit volume) is the same as that of:
Correct Answer: Option A
Explanation:
Energy density = energy/volume. Energy has dimensions [ML²T⁻²], volume [L³], so energy density = [ML²T⁻²]/[L³] = [ML⁻¹T⁻²]. Pressure = force/area = [MLT⁻²]/[L²] = [ML⁻¹T⁻²], identical. Force is [MLT⁻²], power [ML²T⁻³], momentum [MLT⁻¹]. This equivalence explains why pressure appears in Bernoulli's equation alongside kinetic/potential energy density. Memory aid: 'Pressure and energy density share dimensions [ML⁻¹T⁻²]'. This dimensional analysis question tests ability to derive and compare formulas, frequently appearing in competitive exams to assess conceptual depth.
Energy density = energy/volume. Energy has dimensions [ML²T⁻²], volume [L³], so energy density = [ML²T⁻²]/[L³] = [ML⁻¹T⁻²]. Pressure = force/area = [MLT⁻²]/[L²] = [ML⁻¹T⁻²], identical. Force is [MLT⁻²], power [ML²T⁻³], momentum [MLT⁻¹]. This equivalence explains why pressure appears in Bernoulli's equation alongside kinetic/potential energy density. Memory aid: 'Pressure and energy density share dimensions [ML⁻¹T⁻²]'. This dimensional analysis question tests ability to derive and compare formulas, frequently appearing in competitive exams to assess conceptual depth.
Question #2
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In a transistor, the current gain β is defined as:
Correct Answer: Option C
Explanation:
For a bipolar junction transistor (BJT) in common-emitter configuration, DC current gain β = I_C / I_B, where I_C is collector current, I_B base current. Typical β values range 20-200. Option D is α (common-base gain). Memory tip: 'β = collector current / base current; large β means small base current controls large collector current'. This definition-based question tests electronics fundamentals, frequently examined in competitive exams. Always distinguish β (CE configuration) from α (CB configuration) and their relationship: β = α/(1-α).
For a bipolar junction transistor (BJT) in common-emitter configuration, DC current gain β = I_C / I_B, where I_C is collector current, I_B base current. Typical β values range 20-200. Option D is α (common-base gain). Memory tip: 'β = collector current / base current; large β means small base current controls large collector current'. This definition-based question tests electronics fundamentals, frequently examined in competitive exams. Always distinguish β (CE configuration) from α (CB configuration) and their relationship: β = α/(1-α).
Question #3
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The number of significant figures in 3.00 × 10⁸ is
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