Questions covering work, energy principles, and orbital mechanics, including applications in physics exams. Suitable for students studying these topics.
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.
v = gRE2r. r = 17RE, v = 9.8×6.4×10617. v = 3.694×106≈1.92×103m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.9 × 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.
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.
K = GMEm2r. r = 10RE = 6.4×107m. K = 6.67×10−11×6×1024×8002×6.4×107. K = 3.202×10171.28×108≈2.50×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.5 × 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.
Force between two masses: F = Gm2r2 = 6.67×10−1118×18122 = 1.50×10−10N. Two forces at 60°: FR = F2+F2+2F2cos60∘. FR = (1.50×10−10)2(1+1+1) = 1.50×10−103. FR≈2.60×10−10N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.6 × 10⁻¹⁰ N. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and 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.
g decreases above (option 1 correct) and below (option 3 correct) the surface, and is zero at the center (option 2 correct). Option 4 is incorrect as g is maximum at the surface, not below.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
E = −GMm2r for a circular orbit, which is negative due to the bound state. Zero total energy implies the satellite could escape to infinity, which contradicts a stable orbit.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
Kepler’s third law (T2∝a3) shows that planets farther from the Sun (larger semi-major axis a) have longer orbital periods (T), as the period increases with the distance cubed. As per NCERT, applying relevant law/formula with correct units and sign convention leads to They have longer periods. 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.
Escape speed (ve = 2GMR) is independent of the object’s mass (option 1 correct), depends on M and R (option 2 correct), and decreases with altitude (option 4 correct). Option 3 is incorrect as it does depend on the planet.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
Outside a spherical shell, the gravitational force acts as if all the mass is concentrated at the center. Since the mass is non-zero and the distance is finite, the force (F = GMmr2) cannot be zero.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
