#maximum distance

Energy of Satellites and Binding Energy

A projectile is launched at 9km/s from Earth’s surface. What is its maximum distance from the center? (Escape speed = 11

12vi2−ve22 = −ve22REr. 40.5−62.72 = −62.72REr. rRE = 62.7222.22≈2.82. r = 2.82×6.4×106≈1.80×107m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.8 × 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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Energy of Satellites and Binding Energy

A projectile is launched at 1km/s from Earth’s surface. What is its maximum distance from the center? (Escape speed = 11

12vi2−ve22 = −ve22REr. 0.5−62.72 = −62.72REr. rRE = 62.7262.22≈1.008. r = 1.008×6.4×106≈6.45×106m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.5 × 10⁶ 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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Kepler's Laws and Planetary Motion

A projectile launched at 10km/s from Earth reaches a maximum distance of? (Escape speed = 11.2km/s,RE\=6.4×106m)

12vi2−ve22 = −ve22REr. (10)22−(11.2)22 = −(11.2)22REr. 50−62.72 = −62.72REr. rRE = 62.7212.72≈4.93. r≈4.93×6.4×106≈3.15×107m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.2 × 10⁷ 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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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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