This category focuses on questions about how the acceleration due to gravity changes with altitude above the Earth's surface and depth below it, including calculations and conceptual understanding.
ve = 2GMR. ve = 2×6.67×10−11×1.2×10243×106. ve = 5.336×107≈7.3×103m/s = 7.3km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 7.3 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.
g(d) = g(1−d/RE). d = RE/4, g(d) = 9.8(1−1/4) = 9.8×3/4 = 7.35m/s2. Mass: m = 196/9.8 = 20kg. Weight: W = 20×7.35 = 147N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 147 N. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
g(d) = g(1−dRE). At d = RE/2, g(d) = 9.8(1−RE/2RE) = 9.8×0.5 = 4.9m/s2. Mass: m = Wg = 989.8 = 10kg. Weight at depth: W = mg(d) = 10×4.9 = 49N.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
ΔV = −GMEm(1r2−1r1). r1 = 2RE = 1.28×107m, r2 = 4RE = 2.56×107m. ΔV = −6.67×10−11×6×1024×200(12.56×107−11.28×107). ΔV = −8.004×1016(−3.906×10−8)≈3.13×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.1 × 10⁹ J. 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.
Kepler’s third law: Tp2TE2 = ap3aE3. TE = 1year, Tp = 8years, aE = 1.5×1011m. 8212 = ap3(1.5×1011)3. 64 = ap33.375×1033. ap3 = 64×3.375×1033 = 2.16×1035. ap = (2.16×1035)1/3≈6.0×1011m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.0 × 10¹¹ 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.
Kepler’s third law: Tp2TE2 = ap3aE3. TE = 1year, Tp = 9years, aE = 1.5×1011m. 9212 = ap3(1.5×1011)3. 81 = ap33.375×1033. ap3 = 81×3.375×1033 = 2.73375×1035. ap = (2.73375×1035)1/3≈6.49×1011m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.5 × 10¹¹ 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.
V = 0 at r→∞ as a convention, implying that all bound systems (e.g., orbits) have negative potential energy, requiring external work to unbind them to infinity. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Bound systems have negative energy. 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 = 2gRE26RE = 2×9.8×6.4×1066. ve = 2.09×107≈4.57×103m/s≈4.6km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.6 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.
vf2 = vi2−ve2. vf2 = (14)2−(11.2)2 = 196−125.44 = 70.56. vf = 70.56≈8.4km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 8.4 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.
The work done by gravity is independent of the path taken and depends only on the initial and final positions. This path independence defines a conservative force, allowing a potential energy function to be defined.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
V = −GMEmr. r = 1.5RE = 1.5×6.4×106 = 9.6×106m. V = −6.67×10−11×6×1024×10009.6×106. V = −4.17×1010J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -4.2 × 10¹⁰ J. 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.
U = −GMEr. U = −6.67×10−11×6×10241.6×107. U = −2.5×107J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -2.5 × 10⁷ J/kg. 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.
