34 public questions tagged with this topic.
ve = 2gRE25RE = 2×9.8×6.4×1065. ve = 2.509×107≈5.01×103m/s = 5.0km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5.0 km/s. 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.
Escape speed depends on planet parameters (option 1 correct), is independent of direction (option 3 correct), and mass (option 4 correct). Option 2 is incorrect as it decreases with altitude.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
ve = 2GMR. ve = 2×6.67×10−11×9×10232.5×106. ve = 4.801×107≈6.93×103m/s≈6.9km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.9 km/s. 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.
vf2 = vi2−ve2. vf2 = (15.5)2−(11.2)2 = 240.25−125.44 = 114.81. vf = 114.81≈10.71km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 10.7 km/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.
vf2 = vi2−ve2. vf2 = (12)2−(11.2)2 = 144−125.44 = 18.56. vf = 18.56≈4.31km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.3 km/s. 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.
For an object to remain bound, its total mechanical energy (E = KE+PE) must be negative, indicating it lacks sufficient energy to reach infinity where E = 0. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Total energy must be negative. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
ve = 2gRE23RE = 2×9.8×6.4×1063. ve = 4.181×107≈6.47×103m/s≈6.5km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.5 km/s. 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.
Escape speed as ve = 2GMR. The mass m of the object cancels out in the energy conservation equation (12mve2 = GMmR), making ve dependent only on the planet’s mass M and radius R.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
ve = 2GMR. ve = 2×6.67×10−11×4.8×10245×106. ve = 6.403×107≈8.0×103m/s = 8.0km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 8.0 km/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.
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.
ve = 2GMR. ve = 2×6.67×10−11×3.6×10245×106. ve = 9.607×107≈9.80×103m/s≈9.8km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 9.8 km/s. 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.
vf2 = vi2−ve2. vf2 = (11.5)2−(11.2)2 = 132.25−125.44 = 6.81. vf = 6.81≈2.61km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.6 km/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.
