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Kepler’s third law: the square of the orbital period (T2) is proportional to the cube of the semi-major axis (a3), i.e., T2∝a3. This relates time and distance for planetary motion.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Energy conservation: 12mvi2−GMEmRE = −GMEmr. ve2 = 2GMERE, so GMERE = ve22. vi22−ve22 = −ve22REr. (8)22−(11.2)22 = −(11.2)22REr. 32−62.72 = −62.72REr. rRE = 62.7230.72≈2.04. r = 2.04×6.4×106≈1.31×107m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.3 × 10⁷ m. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
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