19 public questions tagged with this topic.
U = −GMEr. U = −6.67×10−11×6×10241.28×107. U = −3.125×107J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -3.1 × 10⁷ J/kg. 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.
Distance to 20kg: 20−9 = 11m. U = −Gm1r1−Gm2r2. U = −6.67×10−11(109+2011). U = −6.67×10−11(1.111+1.818)≈−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.
4 sides: r = 7m, 2 diagonals: r = 72m. V = −4Gm27−2Gm272. V = −6.67×10−11×49(47+272). V = −3.2683×10−9(0.571+0.202)≈−2.53×10−9J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -2.5 × 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.
As altitude increases, r (distance from Earth’s center) increases, reducing the magnitude of the negative term −GMmr, making V less negative. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Distance from the center increases. 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.
Distance to 6kg: 6−2 = 4m. U = −Gm1r1−Gm2r2. U = −6.67×10−11(32+64). U = −6.67×10−11(1.5+1.5) = −2.001×10−10J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -2.0 × 10⁻¹⁰ J/kg. 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.
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.
Gravitational potential energy as V = −GMmr, with zero at infinity. For a bound system (e.g., orbit), the negative value indicates that work must be done to separate the objects to infinity, reflecting gravitational attraction.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
3 pairs: V = −3Gm2r. V = −36.67×10−11×5×54. V = −3×4.169×10−11 = −1.25×10−10J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.2 × 10⁻¹⁰ J. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
V = −GMmr, which is negative (option 1 correct), zero at infinity (option 2 correct), and decreases as r decreases (option 4 correct). Option 3 is incorrect as it is not positive when bound.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
3 pairs: V = −3Gm2r. V = −36.67×10−11×6×68. V = −3×3.0015×10−11 = −9.0×10−11J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -9.0 × 10⁻¹¹ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
V = −GMmr, which is negative for bound systems and decreases (becomes more negative) as r decreases, making option 3 correct. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It becomes more negative as objects approach. 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.
