11 public questions tagged with this topic.
3 pairs: V = −3Gm2r. V = −36.67×10−11×2×21. V = −3×2.668×10−10 = −8.004×10−10J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -8.0 × 10⁻¹⁰ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
U = −GMEr. U = −6.67×10−11×6×10243.84×107. U = −1.0417×107J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.0 × 10⁷ J/kg. 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.
4 sides: r = 6m, 2 diagonals: r = 62m. V = −4Gm26−2Gm262. V = −6.67×10−11×25(46+262). V = −1.6675×10−9(0.667+0.236)≈−1.51×10−9J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.5 × 10⁻⁹ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
4 sides: r = 5m, 2 diagonals: r = 52m. V = −4Gm25−2Gm252. V = −6.67×10−11×16(45+252). V = −1.067×10−9(0.8+0.283)≈−1.15×10−9J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.2 × 10⁻⁹ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and 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.
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.
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.
Kepler’s third law: Tp2TE2 = ap3aE3. TE = 1year, Tp = 3years, aE = 1.5×1011m. 3212 = ap3(1.5×1011)3. 9 = ap33.375×1033. ap3 = 9×3.375×1033 = 3.0375×1034. ap = (3.0375×1034)1/3≈3.12×1011m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.2 × 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.
Distance to 16kg: 16−7 = 9m. U = −Gm1r1−Gm2r2. U = −6.67×10−11(87+169). U = −6.67×10−11(1.143+1.778)≈−1.95×10−10J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.9 × 10⁻¹⁰ J/kg. 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.
M = 4π2r3GT2. T = 18×3600 = 64800s, T2 = 4.199×109s2. r3 = (7×107)3 = 3.43×1023m3. M = 4×(3.14)2×3.43×10236.67×10−11×4.199×109. M = 1.353×10252.801×10−1≈4.83×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.9 × 10²⁵ 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.
