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Energy of Satellites and Binding Energy

Practice questions on the energy concepts related to satellites in orbit, including kinetic, potential, and total energy, as well as binding energy and escape velocity.

24 questions

Energy of Satellites and Binding Energy

Two masses 4kg and 8kg are 8m apart. What is the gravitational potential at a point 3m from the 4kg mass? (G\=6.67×10−11

Distance to 8kg: 8−3 = 5m. U = −Gm1r1−Gm2r2. U = −6.67×10−11(43+85). U = −6.67×10−11(1.333+1.6) = −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 C is scientifically correct.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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Energy of Satellites and Binding Energy

What is the primary reason the gravitational force inside a uniform spherical shell is zero?

Inside a uniform spherical shell, the gravitational forces from all mass elements cancel out due to symmetry, resulting in a net force of zero at any internal point. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Forces cancel due to symmetry. 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.

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Energy of Satellites and Binding Energy

What causes the elliptical shape of planetary orbits according to Newton’s theory?

The inverse-square law (F∝1/r2) leads to elliptical orbits as a general solution to the two-body problem, matching Kepler’s first law, unlike a linear force which would produce circular orbits. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Inverse-square gravitational force. 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.

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Energy of Satellites and Binding Energy

What is the escape speed from a planet of mass 4.8×1024kg and radius 5×106m? (G\=6.67×10−11N m2/kg2)

ve = 2GMR. ve = 2×6.67×10−11×4.8×10245×106. ve = 6.403×107≈8.0×103m/s = 8.0km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 8.0 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.

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Energy of Satellites and Binding Energy

Four 9kg masses form a square of side 9m. What is the potential energy of the system? (G\=6.67×10−11N m2/kg2)

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.

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Energy of Satellites and Binding Energy

Which of the following statements is incorrect about gravitational potential energy?

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.

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Energy of Satellites and Binding Energy

What is the gravitational potential due to Earth at 1.28×107m from its center? (ME\=6×1024kg,G\=6.67×10−11N m2/kg2)

U = −GMEr. U = −6.67×10−11×6×10241.28×107. U = −3.125×107J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -3.1 × 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.

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Energy of Satellites and Binding Energy

Two masses 10kg and 20kg are 20m apart. What is the gravitational potential at a point 9m from the 10kg mass? (G\=6.67×1

Distance to 20kg: 20−9 = 11m. U = −Gm1r1−Gm2r2. U = −6.67×10−11(109+2011). U = −6.67×10−11(1.111+1.818)≈−1.95×10−10J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.9 × 10⁻¹⁰ 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.

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Energy of Satellites and Binding Energy

What is the gravitational force on a 10kg mass 8m from the center of a spherical shell of mass 450kg and radius 6m? (G\=

Outside shell: F = GMmr2. F = 6.67×10−11×450×1082. F = 3.0015×10−864≈4.69×10−10N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.7 × 10⁻¹⁰ N. 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.

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Energy of Satellites and Binding Energy

How much energy is required to move a 500kg satellite from 5RE to 10RE from Earth’s center? (ME\=6×1024kg,RE\=6.4×106m,G

ΔE = −GMEm(1r2−1r1). r1 = 3.2×107m, r2 = 6.4×107m. ΔE = −6.67×10−11×6×1024×500(16.4×107−13.2×107). ΔE = −2.001×1017(−1.5625×10−8)≈3.13×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.1 × 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.

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