20 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.
g(h) = g(1+h/RE)2. h = RE/3, 1+h/RE = 4/3. g(h) = 9.8(4/3)2 = 9.8×916 = 5.51m/s2. Mass: m = 147/9.8 = 15kg. Weight: W = 15×5.51≈82.7N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 83 N. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
g(h) = g0(1+h/RE)2. 5.88 = 9.8(1+h/RE)2. (1+h/RE)2 = 1.667. 1+h/RE = 1.667≈1.291. h/RE = 0.291. h = 0.291×6.4×106≈1.86×106m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.9 × 10⁶ m. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
g(h) = g(1+h/RE)2. h = 3RE/4, 1+h/RE = 1+3/4 = 7/4. g(h) = 9.8(7/4)2 = 9.8×1649 = 3.2m/s2. Mass: m = 294/9.8 = 30kg. Weight: W = 30×3.2 = 96N.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
ve = 2gRE25RE = 2×9.8×6.4×1065. ve = 2.509×107≈5.01×103m/s = 5.0km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5.0 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.
K = GMEm2r. r = 11RE = 7.04×107m. K = 6.67×10−11×6×1024×9002×7.04×107. K = 3.602×10171.408×108≈2.56×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.6 × 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.
K = GMEm2r. r = 3RE = 1.92×107m. K = 6.67×10−11×6×1024×1502×1.92×107. K = 6.003×10163.84×107≈1.56×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.6 × 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.
K = GMEm2r. r = 7RE = 4.48×107m. K = 6.67×10−11×6×1024×5002×4.48×107. K = 2.001×10178.96×107≈2.23×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.3 × 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.
E = −GMEm2r. r = 18RE = 1.152×108m. E = −6.67×10−11×6×1024×11002×1.152×108. E = −4.402×10172.304×108≈−1.91×109J. 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 A 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.
v = gRE2r. r = 11RE, v = 9.8×6.4×10611. v = 5.698×106≈2.39×103m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.4 × 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.
E = −GMEm2r. r = 10RE = 6.4×107m. E = −6.67×10−11×6×1024×7002×6.4×107. E = −2.801×10171.28×108≈−2.19×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -2.2 × 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.
