37 public questions tagged with this topic.
v = gRE2r. r = 2.5RE, v = 9.8×6.4×1062.5. v = 2.509×107≈5.01×103m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5.0 × 10³ m/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.
v = gRE2r. r = 19RE, v = 9.8×6.4×10619. v = 3.301×106≈1.82×103m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.8 × 10³ m/s. 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.
T2∝r3 for satellites. A higher orbit (larger r) increases T2 by r3, so the period T increases as the radius grows, reflecting weaker gravitational pull at greater distances. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Gravitational force decreases. 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 = 2.56×107m, r2 = 5.12×107m. ΔE = −6.67×10−11×6×1024×100(15.12×107−12.56×107). ΔE = −4.002×1016(−1.953×10−8)≈7.82×108J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 7.8 × 10⁸ 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.
T2 = k(RE+h)3, where k = 4π2GME. For h = 0, T0 = 84min, T02 = kRE3. For h = RE, r = 2RE, T2 = k(2RE)3 = 8kRE3. T = 8T0 = 2.828×84≈237min.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
E = −GMEm2r. r = 14RE = 8.96×107m. E = −6.67×10−11×6×1024×9002×8.96×107. E = −3.602×10171.792×108≈−2.01×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -2.0 × 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.
ΔE = −GMEm(1r2−1r1). r1 = 3RE = 1.92×107m, r2 = 6RE = 3.84×107m. ΔE = −6.67×10−11×6×1024×300(13.84×107−11.92×107). ΔE = −1.201×1017(−2.604×10−8)≈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 B is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
v = gRE2r. r = 3RE, v = 9.8×6.4×1063. v = 2.09×107≈4.57×103m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.6 × 10³ m/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.
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.
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.
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.
v = gRE2r. r = 7RE, v = 9.8×6.4×1067. v = 8.966×106≈2.99×103m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.0 × 10³ m/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.
