12 public questions tagged with this topic.
T2∝(RE+h)3. T02 = kRE3, h = 7RE, r = 8RE. T2 = k(8RE)3 = 512kRE3. T = T0512 = 89×22.63≈2014min. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2010 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.
ve = 2gRE23RE = 2×9.8×6.4×1063. ve = 4.181×107≈6.47×103m/s≈6.5km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.5 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.
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.
ve = 2gRE27RE = 2×9.8×6.4×1067. ve = 1.79×107≈4.23×103m/s≈4.2km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.2 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 = 2gRE28RE = 2×9.8×6.4×1068. ve = 1.568×107≈3.96×103m/s≈4.0km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.0 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.
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.
ΔV = −GMEm(1r2−1r1). r1 = 1.92×107m, r2 = 3.84×107m. ΔV = −6.67×10−11×6×1024×4(13.84×107−11.92×107). ΔV = −1.601×1015(−2.604×10−8)≈4.17×107J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.2 × 10⁷ J. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
ΔV = −GMEm(1r2−1r1). r1 = 3.84×107m, r2 = 7.68×107m. ΔV = −6.67×10−11×6×1024×6(17.68×107−13.84×107). ΔV = −2.401×1015(−1.302×10−8)≈3.13×107J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.1 × 10⁷ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
T2∝(RE+h)3. T02 = kRE3, h = 8RE, r = 9RE. T2 = k(9RE)3 = 729kRE3. T = T0729 = 83×27≈2241min. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2250 min. This satisfies dimensional consistency and physical conditions given, so option D is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
T2∝(RE+h)3. T02 = kRE3, h = 4RE, r = 5RE. T2 = k(5RE)3 = 125kRE3. T = T0125 = 88×11.18≈983min. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 990 min. This satisfies dimensional consistency and physical conditions given, so option D is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
K = GMEm2r. r = 9RE = 5.76×107m. K = 6.67×10−11×6×1024×7002×5.76×107. K = 2.801×10171.152×108≈2.43×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.4 × 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.
