Explanation:
v ∝ 1/√r. If r' = 2r, v' = v/√2. Orbital velocity decreases with increasing radius. Memory aid: 'Higher orbit ⇒ slower speed; v ∝ r⁻¹/²'. Proportional reasoning question testing gravitation formula application, frequently appearing in competitive exams without heavy calculation.
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.
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