Questions covering gravitational potential energy, gravitational fields, and their applications in physics. Useful for students preparing for exams involving gravitational concepts.
ve = 2gRE22RE = gRE. ve = 9.8×6.4×106 = 6.272×107. ve≈7.92×103m/s≈7.9km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 7.9 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.
Force between two masses: F = Gm2r2 = 6.67×10−1110×1072 = 1.36×10−10N. Two forces at 60°: FR = F2+F2+2F2cos60∘. FR = (1.36×10−10)2(1+1+1) = 1.36×10−103. FR≈2.36×10−10N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.4 × 10⁻¹⁰ N. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
An object escapes if its total mechanical energy (E = KE+PE) is zero or positive. This occurs when its initial speed equals or exceeds the escape speed (ve = 2GMR), making energy the key factor.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
3 pairs: V = −3Gm2r. V = −36.67×10−11×6×68. V = −3×3.0015×10−11 = −9.0×10−11J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -9.0 × 10⁻¹¹ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
V = −GMmr, which is negative for bound systems and decreases (becomes more negative) as r decreases, making option 3 correct. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It becomes more negative as objects approach. 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.
12vi2−ve22 = −ve22REr. 4.5−62.72 = −62.72REr. rRE = 62.7258.22≈1.077. r = 1.077×6.4×106≈6.89×106m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.9 × 10⁶ m. 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/5, 1+h/RE = 1+1/5 = 6/5. g(h) = 9.8(6/5)2 = 9.8×2536 = 6.81m/s2. Mass: m = 343/9.8 = 35kg. Weight: W = 35×6.81≈238N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 238 N. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
For a uniform sphere, symmetry ensures that the net gravitational force on an external point is equivalent to that of a point mass at the center, as forces from all parts combine accordingly.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
U = −GMEr. U = −6.67×10−11×6×10243.2×107. U = −1.25×107J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.2 × 10⁷ 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, h = 6RE, r = 7RE. T2 = k(7RE)3 = 343kRE3. T = T0343 = 87×18.52≈1611min. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1620 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.
Distance to 22kg: 22−10 = 12m. U = −Gm1r1−Gm2r2. U = −6.67×10−11(1110+2212). U = −6.67×10−11(1.1+1.833)≈−1.96×10−10J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -2.0 × 10⁻¹⁰ J/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.
v = gRE2r. r = 9RE, v = 9.8×6.4×1069. v = 6.964×106≈2.64×103m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.6 × 10³ m/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.
