20 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.
T2∝(RE+h)3. T02 = kRE3, h = 5RE, r = 6RE. T2 = k(6RE)3 = 216kRE3. T = T0216 = 86×14.7≈1264min. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1270 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∝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.
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.
T2∝a3, meaning the period squared is proportional to the semi-major axis cubed, making option 2 correct. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Period squared is proportional to distance cubed. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Kepler’s third law: Tp2TE2 = ap3aE3. TE = 1year, Tp = 7years, aE = 1.5×1011m. 7212 = ap3(1.5×1011)3. 49 = ap33.375×1033. ap3 = 49×3.375×1033 = 1.65375×1035. ap = (1.65375×1035)1/3≈5.49×1011m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5.5 × 10¹¹ m. 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 = 9×86400 = 7.776×105s. T2 = 6.046×1011s2. r3 = (6×108)3 = 2.16×1026m3. M = 4×(3.14)2×2.16×10266.67×10−11×6.046×1011. M = 8.51×10264.033×101≈2.11×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.1 × 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.
Kepler’s third law: T2∝a3, Tp2TE2 = ap3aE3. TE = 1year, Tp = 4years, aE = 1.5×1011m. 4212 = ap3(1.5×1011)3. 16 = ap33.375×1033. ap3 = 16×3.375×1033 = 5.4×1034. ap = (5.4×1034)1/3≈3.78×1011m.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
Kepler’s third law: Tp2TE2 = ap3aE3. TE = 1year, Tp = 6years, aE = 1.5×1011m. 6212 = ap3(1.5×1011)3. 36 = ap33.375×1033. ap3 = 36×3.375×1033 = 1.215×1035. ap = (1.215×1035)1/3≈4.95×1011m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5.0 × 10¹¹ m. 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.
T2∝(RE+h)3. T02 = kRE3, h = 3RE, r = 4RE. T2 = k(4RE)3 = 64kRE3. T = T064 = 90×8 = 720min. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 720 min. 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 = 5×3600 = 18000s, T2 = 3.24×108s2. r3 = (2.5×107)3 = 1.5625×1022m3. M = 4×(3.14)2×1.5625×10226.67×10−11×3.24×108. M = 6.158×10232.161×10−2≈2.85×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.9 × 10²⁵ kg. 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.
T2 = 4π2GMr3. M = 4π2r3GT2. T = 2×3600 = 7200s, T2 = 5.184×107s2. r3 = (2×106)3 = 8×1018m3. M = 4×(3.14)2×8×10186.67×10−11×5.184×107. M = 3.155×10203.458×10−3≈9.12×1022kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 9.1 × 10²² kg. 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.
