v_e = √(2GM/R): depends on planet's M and R, independent of projectile mass or launch direction. Memory tip: 'v_e ∝ √(M/R); property of planet, not projectile'. Gravitation concept frequently tested in competitive exams.
Explanation:
Convert speeds: 18 km/h = 5 m/s, 36 km/h = 10 m/s. Using v = u + at => a = (10-5)/5 = 1 m/s². Distance s = ut + ½at² = 5×5 + ½×1×25 = 25 + 12.5 = 37.5 m. Also using average velocity: (5+10)/2 × 5 = 7.5×5 = 37.5 m. Answer A.
Explanation:
Latent heat of vaporization is the heat required to change unit mass from liquid to vapor at constant temperature (boiling point). For water, it's approximately 2260 kJ/kg. Latent heat of fusion applies to solid-liquid transition. Specific heat relates to temperature change without phase change. Thermal conductivity measures heat transfer rate through conduction. Memory aid: 'Vaporization = liquid to gas; fusion = solid to liquid'. This definition-based question tests precise terminology, crucial for thermodynamics sections in competitive exams where distractors often mix phase change terms.
Explanation:
By conservation of angular momentum: I1w1 = I2w2. Moment of inertia of a solid sphere is 2/5 MR^2. So, (R1^2) * (2pi/T1) = (R2^2) * (2pi/T2). If radius halves, R2 = R1/2. R1^2 / T1 = (R1/2)^2 / T2. T2 = T1 / 4. A day is 24 hours, so 24/4 = exactly 6 hours.
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