The dimensional formula of surface tension is MCQ with Answer and Explanation
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Question #1
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If the intensity of a sound is mathematically increased by a factor of 100, its loudness level in decibels (dB) increases strictly by:
Correct Answer: Option D
Explanation:
The loudness level in decibels is calculated as L = 10 * log10(I / I0). If intensity I becomes 100I, the new level L' = 10 * log10(100I / I0) = 10 * [log10(100) + log10(I / I0)] = 10 * [2 + L/10] = 20 + L. Therefore, the loudness explicitly increases by 20 dB.
The loudness level in decibels is calculated as L = 10 * log10(I / I0). If intensity I becomes 100I, the new level L' = 10 * log10(100I / I0) = 10 * [log10(100) + log10(I / I0)] = 10 * [2 + L/10] = 20 + L. Therefore, the loudness explicitly increases by 20 dB.
Question #2
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Which of the following is a derived unit?
Question #3
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The dimensional formula of angular momentum is:
Correct Answer: Option A
Explanation:
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.
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.
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