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#Earth

10 public questions tagged with this topic.

Forced Oscillations and Resonance

A simple pendulum has a period of \( 1 \, \text{s} \) on Earth (\( g = 9.8 \, \text{m/s}^2 \)). What is its period on th

**Driven system** exhibits amplitude-frequency response peaking at resonance, phase shift between drive and displacement varying 0° to 180° across resonance. Forced oscillations sustain motion against damping, amplitude controlled by detuning |ω_d - ω₀| and damping strength b. T ∝ (1/√(g)) . (TMₒₒₙ/TEₐrth) = √((gEₐrth/gMₒₒₙ)) = √((9.8/1.63)) ≈ √(6) ≈ 2.45 . TMₒₒₙ = 1 × 2.45 ≈ 2.45 s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 2.45 s follows, reflecting SHM dependence on amplitude A, ω and system parameters.

Ref: NCERT > Physics Book > Oscillations > Forced Oscillations and Resonance

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Orbital Velocity and Time Period

A 1000kg satellite orbits Earth at 16RE from the center. What is its total energy? (ME\=6×1024kg,RE\=6.4×106m,G\=6.67×10

E = −GMEm2r. r = 16RE = 1.024×108m. E = −6.67×10−11×6×1024×10002×1.024×108. E = −4.002×10172.048×108≈−1.95×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.9 × 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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Orbital Velocity and Time Period

How much energy is required to move a 300kg satellite from 7RE to 14RE from Earth’s center? (ME\=6×1024kg,RE\=6.4×106m,G

ΔE = −GMEm(1r2−1r1). r1 = 4.48×107m, r2 = 8.96×107m. ΔE = −6.67×10−11×6×1024×300(18.96×107−14.48×107). ΔE = −1.201×1017(−1.116×10−8)≈1.34×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.3 × 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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Orbital Velocity and Time Period

What is the kinetic energy of a 200kg satellite at 4RE from Earth’s center? (ME\=6×1024kg,RE\=6.4×106m,G\=6.67×10−11N m2

K = GMEm2r. r = 4RE = 2.56×107m. K = 6.67×10−11×6×1024×2002×2.56×107. K = 8.004×10165.12×107≈1.56×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.6 × 10⁹ J. 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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Orbital Velocity and Time Period

What is the gravitational potential due to Earth at 5.12×107m from its center? (ME\=6×1024kg,G\=6.67×10−11N m2/kg2)

U = −GMEr. U = −6.67×10−11×6×10245.12×107. U = −7.8125×106J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -7.8 × 10⁶ 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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Work, Energy and Orbital Mechanics

What is the minimum speed required to escape from a point RE above Earth’s surface? (RE\=6.4×106m,g\=9.8m/s2)

ve = 2GMERE+h = 2gRE22RE = gRE2. ve = 9.8×6.4×1062 = 3.136×107. ve≈5.6×103m/s = 5.6km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5.6 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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ORIGIN OF LIFE

Origin of life on Earth is estimated to be around

3.5 billion years ago reflects key principle in quiz on origin of life, where evolutionary mechanisms shape genetic variation and adaptation. In this context, 3.5 billion years ago aligns with experimental and theoretical evidence from population genetics, behavioral ecology and molecular phylogeny. Textbooks like Campbell Biology, Futuyma Evolution and Hartl Principles illustrate supporting data. Understanding why 3.5 billion years ago fits helps integrate natural selection, drift and species concepts essential for NEET, CSIR-NET and GATE examinations. This concept integrates genetics, ecology and molecular evidence, frequently tested in NEET, GATE and CSIR-NET, highlighting links between genotype,

Ref: NCBI Bookshelf, Molecular Cell Biology, Origin of Life Theories.

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