A geostationary satellite orbits the Earth from: MCQ with Answer and Explanation
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Question #1
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Half-life 5 days. Fraction remaining after 15 days:
Correct Answer: Option D
Explanation:
Number of half-lives n = 15/5 = 3. Fraction = (1/2)³ = 1/8. Exponential decay: N = N₀(1/2)^(t/T). Memory aid: 'After n half-lives: fraction = 1/2ⁿ'. Radioactivity calculation frequently tested in competitive exams with simple half-life arithmetic.
Number of half-lives n = 15/5 = 3. Fraction = (1/2)³ = 1/8. Exponential decay: N = N₀(1/2)^(t/T). Memory aid: 'After n half-lives: fraction = 1/2ⁿ'. Radioactivity calculation frequently tested in competitive exams with simple half-life arithmetic.
Question #2
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The dimension of Planck's constant is same as that of
Correct Answer: Option B
Explanation:
Planck's constant h = E/ν, so its dimensions are [Energy]/[Frequency] = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹]. Angular momentum = mvr = M·LT⁻¹·L = [ML²T⁻¹]. Energy = [ML²T⁻²], linear momentum = [MLT⁻¹], force = [MLT⁻²]. Thus, Planck's constant and angular momentum share dimensions. This is a key dimensional match in quantum mechanics.
Planck's constant h = E/ν, so its dimensions are [Energy]/[Frequency] = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹]. Angular momentum = mvr = M·LT⁻¹·L = [ML²T⁻¹]. Energy = [ML²T⁻²], linear momentum = [MLT⁻¹], force = [MLT⁻²]. Thus, Planck's constant and angular momentum share dimensions. This is a key dimensional match in quantum mechanics.
Question #3
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The refractive index of a medium is 1.5. The speed of light in this medium is:
Correct Answer: Option B
Explanation:
Refractive index n = c/v, where c = 3×10⁸ m/s (vacuum speed). Thus v = c/n = 3×10⁸ / 1.5 = 2×10⁸ m/s. This direct calculation tests optics fundamentals. Memory aid: 'Higher n ⇒ slower light; v = c/n'. Competitive exams frequently test this with common refractive indices. Always use c = 3×10⁸ m/s unless specified; verify units (m/s). This problem assesses basic formula application skills essential for wave optics sections.
Refractive index n = c/v, where c = 3×10⁸ m/s (vacuum speed). Thus v = c/n = 3×10⁸ / 1.5 = 2×10⁸ m/s. This direct calculation tests optics fundamentals. Memory aid: 'Higher n ⇒ slower light; v = c/n'. Competitive exams frequently test this with common refractive indices. Always use c = 3×10⁸ m/s unless specified; verify units (m/s). This problem assesses basic formula application skills essential for wave optics sections.
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