The minimum distance to hear an echo (persistence of hearing 0.1 s, speed 340 m/s) is MCQ with Answer and Explanation
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Question #1
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Which one of the following graphs accurately represents the variation of magnetic field (B) with distance (r) from the exact center of a solid, current-carrying cylindrical wire of radius R?
Correct Answer: Option D
Explanation:
By Ampere's Circuital Law, for a solid wire carrying uniform current, the magnetic field inside (r < R) is B = (mu_0 * I * r) / (2piR^2), meaning B ∝ r (straight line). Outside the wire (r > R), B = (mu_0 * I) / (2pi*r), meaning B ∝ 1/r (rectangular hyperbola). Thus, it increases linearly then decays.
By Ampere's Circuital Law, for a solid wire carrying uniform current, the magnetic field inside (r < R) is B = (mu_0 * I * r) / (2piR^2), meaning B ∝ r (straight line). Outside the wire (r > R), B = (mu_0 * I) / (2pi*r), meaning B ∝ 1/r (rectangular hyperbola). Thus, it increases linearly then decays.
Question #2
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A 10 μF capacitor is charged to 100 V. Energy stored is
Question #3
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A Carnot engine operates between 400 K and 300 K. Its efficiency is:
Correct Answer: Option A
Explanation:
Carnot efficiency η = 1 - T₂/T₁, where T₁ is source temperature, T₂ sink temperature (in Kelvin). Here T₁=400 K, T₂=300 K, so η = 1 - 300/400 = 1 - 0.75 = 0.25 = 25%. This maximum possible efficiency for given temperatures is a fundamental thermodynamics result. Memory tip: 'η_Carnot = 1 - T_cold/T_hot'. Competitive exams frequently test this formula with varying temperatures. Always use absolute temperatures (Kelvin); Celsius would yield incorrect efficiency. This problem assesses understanding of heat engine limitations.
Carnot efficiency η = 1 - T₂/T₁, where T₁ is source temperature, T₂ sink temperature (in Kelvin). Here T₁=400 K, T₂=300 K, so η = 1 - 300/400 = 1 - 0.75 = 0.25 = 25%. This maximum possible efficiency for given temperatures is a fundamental thermodynamics result. Memory tip: 'η_Carnot = 1 - T_cold/T_hot'. Competitive exams frequently test this formula with varying temperatures. Always use absolute temperatures (Kelvin); Celsius would yield incorrect efficiency. This problem assesses understanding of heat engine limitations.
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