Practice problems covering Newton’s law of gravitation, gravitational potential energy, field strength, and real-world applications such as orbital mechanics.
vf2 = vi2−ve2. vf2 = (15.5)2−(11.2)2 = 240.25−125.44 = 114.81. vf = 114.81≈10.71km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 10.7 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.
Near Earth’s surface, gravity is approximately constant (F = mg), and the force acts vertically. Thus, work (W = F⋅Δh) depends only on vertical displacement (Δh), as horizontal motion is perpendicular to the force.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
vf2 = vi2−ve2. vf2 = (12)2−(11.2)2 = 144−125.44 = 18.56. vf = 18.56≈4.31km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.3 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.
At the center (r = 0), the gravitational forces from all mass elements of a uniform sphere cancel out due to symmetry, as the net force from opposite directions balances to zero.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
M = 4π2r3GT2. T = 10×86400 = 8.64×105s. T2 = 7.465×1011s2. r3 = (7×108)3 = 3.43×1026m3. M = 4×(3.14)2×3.43×10266.67×10−11×7.465×1011. M = 1.353×10274.979×101≈2.72×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.7 × 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.
Kepler’s third law: Tp2TE2 = ap3aE3. TE = 1year, Tp = 10years, aE = 1.5×1011m. 10212 = ap3(1.5×1011)3. 100 = ap33.375×1033. ap3 = 100×3.375×1033 = 3.375×1035. ap = (3.375×1035)1/3≈6.96×1011m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 7.0 × 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.
Using Kepler’s third law: T2 = 4π2GMsa3. Rearrange for Ms: Ms = 4π2a3GT2. T = 2×3.156×107 = 6.312×107s. a = 2.25×1011m. T2 = (6.312×107)2 = 3.984×1015s2. a3 = (2.25×1011)3 = 1.139×1033m3. Ms = 4×(3.14)2×1.139×10336.67×10−11×3.984×1015. Ms = 4.49×10342.657×105≈1.69×1030kg.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
ve = 2GMR. ve = 2×6.67×10−11×1.8×10243.5×106. ve = 6.861×107≈8.28×103m/s≈8.3km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 8.3 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.
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.
For an object to remain bound, its total mechanical energy (E = KE+PE) must be negative, indicating it lacks sufficient energy to reach infinity where E = 0. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Total energy must be negative. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Negative total energy (E = KE+PE
Ref: NCERT Class 11 Physics, Thermal Properties and 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.
