Questions covering escape velocity and bound systems, including calculations and theoretical applications. Suitable for physics exam preparation.
The negative sign indicates that gravitational potential energy is zero at infinite separation (r→∞) and decreases (becomes more negative) as objects approach each other. It reflects the attractive nature of gravity, where work must be done to separate masses.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
The net gravitational force inside a uniform hollow spherical shell is zero due to symmetry, making option 2 correct. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It is zero everywhere inside. 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.
E = −GMEm2r. r = 3RE = 3×6.4×106 = 1.92×107m. E = −6.67×10−11×6×1024×1002×1.92×107. E = −4.002×10163.84×107≈−1.04×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.0 × 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.
nan As per NCERT, applying relevant law/formula with correct units and sign convention leads to It measured the gravitational constant. 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 = 6×86400 = 5.184×105s. T2 = 2.689×1011s2. r3 = (4×108)3 = 6.4×1025m3. M = 4×(3.14)2×6.4×10256.67×10−11×2.689×1011. M = 2.523×10261.794×101≈1.41×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.4 × 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.
M = 4π2r3GT2. T = 11×86400 = 9.504×105s. T2 = 9.028×1011s2. r3 = (8×108)3 = 5.12×1026m3. M = 4×(3.14)2×5.12×10266.67×10−11×9.028×1011. M = 2.019×10276.022×101≈3.35×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.4 × 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.
M = 4π2r3GT2. T = 12×86400 = 1.0368×106s. T2 = 1.075×1012s2. r3 = (9×108)3 = 7.29×1026m3. M = 4×(3.14)2×7.29×10266.67×10−11×1.075×1012. M = 2.875×10277.171×101≈4.01×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.0 × 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.
As altitude increases, r (distance from Earth’s center) increases, reducing the magnitude of the negative term −GMmr, making V less negative. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Distance from the center increases. 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∝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.
U = −GMEr. U = −6.67×10−11×6×10249.6×106. U = −4.002×10149.6×106 = −4.17×107J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -4.2 × 10⁷ 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.
nan As per NCERT, applying relevant law/formula with correct units and sign convention leads to Force varies as inverse-square. 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.
nan As per NCERT, applying relevant law/formula with correct units and sign convention leads to It weakens with distance. 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.
