27 public questions tagged with this topic.
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.
4 sides: r = 9m, 2 diagonals: r = 92m. V = −4Gm29−2Gm292. V = −6.67×10−11×81(49+292). V = −5.4027×10−9(0.444+0.157)≈−3.25×10−9J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -3.2 × 10⁻⁹ J. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
It’s negative (option 1 correct), zero at infinity (option 2 correct), and conservative (option 3 correct). Option 4 is incorrect as it depends on distance, not mass alone. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It depends only on mass. 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.
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.
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 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.
V = −GMmr, with the convention that V = 0 at r→∞. As r increases, 1r decreases, making V less negative and approaching zero. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It is defined as zero at infinity. 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.
ΔE = −GMEm(1r2−1r1). r1 = 2.56×107m, r2 = 5.12×107m. ΔE = −6.67×10−11×6×1024×100(15.12×107−12.56×107). ΔE = −4.002×1016(−1.953×10−8)≈7.82×108J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 7.8 × 10⁸ 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.
ΔV = −GMEm(1r2−1r1). r1 = 4.48×107m, r2 = 8.96×107m. ΔV = −6.67×10−11×6×1024×7(18.96×107−14.48×107). ΔV = −2.801×1015(−1.116×10−8)≈3.13×107J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.1 × 10⁷ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
E = −GMEm2r. r = 14RE = 8.96×107m. E = −6.67×10−11×6×1024×9002×8.96×107. E = −3.602×10171.792×108≈−2.01×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -2.0 × 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.
