A 10 kg object is lifted to 5 m and then allowed to fall. Kinetic energy just before hitting ground (g=10) is MCQ with Answer and Explanation
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Question #1
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The phenomenon of beats can be observed when two sound waves have:
Correct Answer: Option C
Explanation:
Beats occur due to interference of two waves with slightly different frequencies (Δf small, typically < 10 Hz for audible beats). The beat frequency is |f₁ - f₂|, causing periodic loudness variation. Same frequency (A, B) produces steady interference (no beats); very different frequencies (D) produce rapid fluctuations not perceived as beats. Memory aid: 'Beats: |f₁ - f₂| small ⇒ audible pulsations; used in tuning'. This wave phenomenon question tests superposition understanding, frequently examined in competitive exams. Always link beat perception to frequency difference magnitude; competitive exams often test qualitative conditions for observable beats.
Beats occur due to interference of two waves with slightly different frequencies (Δf small, typically < 10 Hz for audible beats). The beat frequency is |f₁ - f₂|, causing periodic loudness variation. Same frequency (A, B) produces steady interference (no beats); very different frequencies (D) produce rapid fluctuations not perceived as beats. Memory aid: 'Beats: |f₁ - f₂| small ⇒ audible pulsations; used in tuning'. This wave phenomenon question tests superposition understanding, frequently examined in competitive exams. Always link beat perception to frequency difference magnitude; competitive exams often test qualitative conditions for observable beats.
Question #2
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The escape velocity from Earth's surface is approximately 11.2 km/s. If a planet has twice Earth's radius and same density, its escape velocity will be:
Correct Answer: Option C
Explanation:
Escape velocity v_e = √(2GM/R). Mass M = density ρ × volume = ρ×(4/3)πR³. Thus v_e = √(2Gρ×4/3πR³ / R) = √(8GρπR²/3) ∝ R√ρ. Given same density and R_planet = 2R_earth, v_e ∝ R, so v_e_planet = 2 × 11.2 = 22.4 km/s. This derivation shows escape velocity scales linearly with radius for constant density. Memory tip: v_e ∝ √(M/R) and M ∝ R³ for constant ρ, so v_e ∝ R. Such proportional reasoning questions test conceptual grasp of gravitation formulas in competitive exams without heavy calculation.
Escape velocity v_e = √(2GM/R). Mass M = density ρ × volume = ρ×(4/3)πR³. Thus v_e = √(2Gρ×4/3πR³ / R) = √(8GρπR²/3) ∝ R√ρ. Given same density and R_planet = 2R_earth, v_e ∝ R, so v_e_planet = 2 × 11.2 = 22.4 km/s. This derivation shows escape velocity scales linearly with radius for constant density. Memory tip: v_e ∝ √(M/R) and M ∝ R³ for constant ρ, so v_e ∝ R. Such proportional reasoning questions test conceptual grasp of gravitation formulas in competitive exams without heavy calculation.
Question #3
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A metal spoon placed in a hot cup of tea gets hot due to
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