21 public questions tagged with this topic.
g(d) = g0(1−d/RE). 6.86 = 9.8(1−d/RE). 1−d/RE = 0.7. d/RE = 0.3. d = 0.3×6.4×106 = 1.92×106m. 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.
ΔE = −GMEm(1r2−1r1). r1 = 5.12×107m, r2 = 1.024×108m. ΔE = −6.67×10−11×6×1024×400(11.024×108−15.12×107). ΔE = −1.601×1017(−9.766×10−9)≈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 B is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
g(h) = g(1+h/RE)2. h = RE/6, 1+h/RE = 1+1/6 = 7/6. g(h) = 9.8(7/6)2 = 9.8×3649 = 7.2m/s2. Mass: m = 392/9.8 = 40kg. Weight: W = 40×7.2 = 288N.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
M = 4π2r3GT2. T = 15×3600 = 54000s, T2 = 2.916×109s2. r3 = (6×107)3 = 2.16×1023m3. M = 4×(3.14)2×2.16×10236.67×10−11×2.916×109. M = 8.51×10241.948×10−1≈4.37×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.4 × 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.
g(d) = g0(1−d/RE). 7.35 = 9.8(1−d/RE). 1−d/RE = 0.75. d/RE = 0.25. d = 0.25×6.4×106 = 1.6×106m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.6 × 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.
K = GMEm2r. r = 8RE = 5.12×107m. K = 6.67×10−11×6×1024×6002×5.12×107. K = 2.401×10171.024×108≈2.34×109J. 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 C is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
Outside shell: F = GMmr2. F = 6.67×10−11×350×972. F = 2.101×10−849≈4.29×10−10N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.3 × 10⁻¹⁰ N. 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.
Distance to 18kg: 18−8 = 10m. U = −Gm1r1−Gm2r2. U = −6.67×10−11(98+1810). U = −6.67×10−11(1.125+1.8)≈−1.95×10−10J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.9 × 10⁻¹⁰ 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.
T2∝(RE+h)3. T02 = kRE3, T2 = k(3RE)3 = 27kRE3. T = T027 = 100×5.196≈520min. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 520 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.
K = GMEm2r. r = 6RE = 3.84×107m. K = 6.67×10−11×6×1024×4002×3.84×107. K = 1.601×10177.68×107≈2.08×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.1 × 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.
Outside a shell, F = GMmr2. F = 6.67×10−11×500×1032. F = 3.335×10−79≈3.71×10−8N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.7 × 10⁻⁸ N. 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 = 2GMR. ve = 2×6.67×10−11×1.2×10243×106. ve = 5.336×107≈7.3×103m/s = 7.3km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 7.3 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.
