Questions on Kepler's laws and planetary motion, including applications and calculations. Designed for students preparing for physics or astronomy exams.
T2∝(RE+h)3. T02 = kRE3, h = 9RE, r = 10RE. T2 = k(10RE)3 = 1000kRE3. T = T01000 = 82×31.62≈2593min. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2590 min. 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.
K = GMEm2r. r = 5RE = 3.2×107m. K = 6.67×10−11×6×1024×3002×3.2×107. K = 1.201×10176.4×107≈1.88×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.9 × 10⁹ 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.
M = 4π2r3GT2. T = 13×86400 = 1.1232×106s. T2 = 1.262×1012s2. r3 = (1.0×109)3 = 1.0×1027m3. M = 4×(3.14)2×10276.67×10−11×1.262×1012. M = 3.947×10278.418×101≈4.69×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.7 × 10²⁵ 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.
A stable circular orbit requires the gravitational force (GMEmr2) to equal the centripetal force (mv2r), balancing the forces to maintain constant radius and speed. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Balance of gravitational and centripetal forces. 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 first law (law of orbits) describes planetary orbits as ellipses with the Sun at one focus, not circles (a special case of an ellipse). This deviation from circular motion reflects the real dynamics of gravitational interaction.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: 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.
The total energy E = −GMm2r is negative because the potential energy (−GMmr) is negative and twice the magnitude of the positive kinetic energy (GMm2r). This negative value indicates a bound system.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: 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.
12vi2−12ve2 = 12vf2. vf2 = (13)2−(11.2)2 = 169−125.44 = 43.56. vf = 43.56≈6.6km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.6 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.
ve = 2gR. ve = 2×4.9×3.2×106 = 3.136×107. ve≈5.6×103m/s = 5.6km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5.6 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.
ΔE = −GMEm(1r2−1r1). r1 = 6.4×107m, r2 = 1.28×108m. ΔE = −6.67×10−11×6×1024×600(11.28×108−16.4×107). ΔE = −2.401×1017(−7.8125×10−9)≈1.88×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.9 × 10⁹ 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.
