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#physics practice question

18 public questions tagged with this topic.

Kepler's Laws and Planetary Motion

Four 5kg masses form a square of side 6m. What is the potential energy of the system? (G\=6.67×10−11N m2/kg2)

4 sides: r = 6m, 2 diagonals: r = 62m. V = −4Gm26−2Gm262. V = −6.67×10−11×25(46+262). V = −1.6675×10−9(0.667+0.236)≈−1.51×10−9J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.5 × 10⁻⁹ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Kepler's Laws and Planetary Motion

A satellite orbits Earth at 7RE from the center. What is its orbital speed? (g\=9.8m/s2,RE\=6.4×106m)

v = gRE2r. r = 7RE, v = 9.8×6.4×1067. v = 8.966×106≈2.99×103m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.0 × 10³ m/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.

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Kepler's Laws and Planetary Motion

A planet orbits the Sun with a period of 7 years. If Earth’s orbital radius is 1.5×1011m, what is its semi-major axis?

Kepler’s third law: Tp2TE2 = ap3aE3. TE = 1year, Tp = 7years, aE = 1.5×1011m. 7212 = ap3(1.5×1011)3. 49 = ap33.375×1033. ap3 = 49×3.375×1033 = 1.65375×1035. ap = (1.65375×1035)1/3≈5.49×1011m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5.5 × 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.

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Kepler's Laws and Planetary Motion

A moon orbits a planet with a period of 9 days and radius 6×108m. What is the planet’s mass? (G\=6.67×10−11N m2/kg2,1day

M = 4π2r3GT2. T = 9×86400 = 7.776×105s. T2 = 6.046×1011s2. r3 = (6×108)3 = 2.16×1026m3. M = 4×(3.14)2×2.16×10266.67×10−11×6.046×1011. M = 8.51×10264.033×101≈2.11×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.1 × 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.

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Kepler's Laws and Planetary Motion

Four 4kg masses form a square of side 5m. What is the potential energy of the system? (G\=6.67×10−11N m2/kg2)

4 sides: r = 5m, 2 diagonals: r = 52m. V = −4Gm25−2Gm252. V = −6.67×10−11×16(45+252). V = −1.067×10−9(0.8+0.283)≈−1.15×10−9J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.2 × 10⁻⁹ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Work, Energy and Orbital Mechanics

A body is launched from Earth at 13.5km/s. What is its speed at infinity? (Escape speed = 11.2km/s)

vf2 = vi2−ve2. vf2 = (13.5)2−(11.2)2 = 182.25−125.44 = 56.81. vf = 56.81≈7.54km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 7.5 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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Work, Energy and Orbital Mechanics

How much energy is required to move a 500kg satellite from 9RE to 18RE from Earth’s center? (ME\=6×1024kg,RE\=6.4×106m,G

ΔE = −GMEm(1r2−1r1). r1 = 5.76×107m, r2 = 1.152×108m. ΔE = −6.67×10−11×6×1024×500(11.152×108−15.76×107). ΔE = −2.001×1017(−8.681×10−9)≈1.74×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.7 × 10⁹ J. 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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Work, Energy and Orbital Mechanics

A 800kg satellite orbits Earth at 12RE from the center. What is its total energy? (ME\=6×1024kg,RE\=6.4×106m,G\=6.67×10−

E = −GMEm2r. r = 12RE = 7.68×107m. E = −6.67×10−11×6×1024×8002×7.68×107. E = −3.202×10171.536×108≈−2.08×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -2.1 × 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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Work, Energy and Orbital Mechanics

What is the gravitational force on a 2kg mass inside a hollow spherical shell of mass 1000kg and radius 1m?

Inside a hollow spherical shell, the gravitational force is zero due to symmetry (as per the shell theorem). F = 0N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 0 N. 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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Potential Energy of Mass Systems

A body is launched from Earth at 11.8km/s. What is its speed at infinity? (Escape speed = 11.2km/s)

vf2 = vi2−ve2. vf2 = (11.8)2−(11.2)2 = 139.24−125.44 = 13.8. vf = 13.8≈3.71km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.7 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.

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Variation of g with Height and Depth

Which of the following statements is correct about Kepler’s laws?

Kepler’s laws apply to any central force following an inverse-square law (e.g., gravitation), making option 4 correct as they describe planetary motion around the Sun. They require circular orbits 1 2 3 4 Correct ans: Option (4) They apply only to Earth They depend on planet mass They apply to inverse-square forces 4

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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