#Earth's radius

Gravitational Effects and Applications

A satellite orbits Earth at a height equal to RE/2. What is its orbital speed? (g\=9.8m/s2,RE\=6.4×106m)

r = RE+RE2 = 1.5RE. v = GMEr = gRE21.5RE = gRE1.5. v = 9.8×6.4×1061.5 = 4.181×107. v≈6.47×103m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.5 × 10³ m/s. 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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Variation of g with Height and Depth

A satellite orbits Earth at 15RE from the center. What is its orbital speed? (g\=9.8m/s2,RE\=6.4×106m)

v = gRE2r. r = 15RE, v = 9.8×6.4×10615. v = 4.181×106≈2.04×103m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.0 × 10³ m/s. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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Variation of g with Height and Depth

At what depth below Earth’s surface is g reduced to 5.39m/s2? (g0\=9.8m/s2,RE\=6.4×106m)

g(d) = g0(1−d/RE). 5.39 = 9.8(1−d/RE). 1−d/RE = 0.55. d/RE = 0.45. d = 0.45×6.4×106 = 2.88×106m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.9 × 10⁶ m. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Universal Law of Gravitation

A projectile is launched at 6km/s from Earth’s surface. What is its maximum distance from the center? (Escape speed = 11

12vi2−ve22 = −ve22REr. 18−62.72 = −62.72REr. rRE = 62.7244.72≈1.40. r = 1.40×6.4×106≈8.96×106m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 9.0 × 10⁶ m. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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