Explanation:
Kinetic energy KE = p²/(2m), where p is momentum. Thus p = √(2m·KE). If KE becomes 4 times, p_new = √(2m·4KE) = 2√(2m·KE) = 2p_initial. Hence momentum doubles. This relationship shows momentum scales with square root of kinetic energy for constant mass. Memory tip: p ∝ √KE when mass constant. This conceptual link between momentum and kinetic energy is frequently tested in competitive exams to assess depth of understanding beyond rote formula memorization. Always derive relationships when direct formulas aren't recalled.
Explanation:
Transformer voltage ratio: V_s/V_p = N_s/N_p, where N is number of turns. Thus V_s = V_p × (N_s/N_p) = 120 V × (200/100) = 240 V. This assumes ideal transformer (no losses). Step-up transformer (N_s > N_p) increases voltage. Memory aid: 'Turns ratio = voltage ratio'. This direct formula application is frequent in competitive exams. Always verify if transformer is step-up or step-down from turn counts. Note: Current ratio is inverse: I_s/I_p = N_p/N_s for power conservation (V_pI_p = V_sI_s).
Explanation:
The angle of dip is the angle the Earth's total magnetic field vector makes with the horizontal surface. At the magnetic equator, the magnetic field lines are perfectly parallel to the ground (0 degrees). At the magnetic poles, the field lines plunge strictly vertically downward (or upward) into the ground, making a 90-degree angle with the horizontal.
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