Learn about the mass and density of Earth with detailed explanations, FAQs, and MCQs. Essential study material for JEE, NEET, and CBSE Class 11 exams.
Mass of Earth
The mass of the Earth is determined using Newton’s law of gravitation and Cavendish’s experiment, where:
g = GM/R2
M = gR2/G
Where,
M = Mass of Earth
g = Acceleration due to gravity (9.81 m/s²)
R = Radius of Earth (~6,371 km)
G = Gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²)
Put constant values in the equation, we get,
M = 5.972 × 10²⁴ kg
Density of Earth
Earth is assumed to be a uniform solid sphere with a mean density (ρ). We know that,
Density = mass/volume
Then, ρ = M/[4/3 πR3]
M = ρ × [4/3 πR3]
We know that g = GM/R2.
On substituting the values of M, we get,
g = 4/3 [πρRG]
At any distance ‘r’ from the centre of the earth,
g = 4/3 [πρRG]
Density of Earth is given by
ρ = 3g/4πGR
g = Acceleration due to gravity (9.81 m/s²)
R = Radius of Earth (~6,371 km)
G = Gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²)
Put constant values in the equation, we get the average density of Earth is
ρ = 5,515 kg/m3
Important Question-Answers on Mass and Density of Earth
Q1: What is the mass of the Earth?
A: The mass of the Earth is approximately 5.972 × 10²⁴ kg.
Q2: What is the density of the Earth?
A: The average density of Earth is 5,515 kg/m³.
Q3: How is the mass of the Earth determined?
A: The mass of the Earth is determined using Newton’s law of gravitation and Cavendish’s experiment, where:
M = gR2/G
Where,
M = Mass of Earth
g = Acceleration due to gravity (9.81 m/s²)
R = Radius of Earth (~6,371 km)
G = Gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²)
Q4: Why is the Earth’s density not uniform?
A: The Earth consists of different layers (crust, mantle, and core) with varying densities. The core, mainly composed of iron and nickel, is denser than the outer layers.
Q5: What is the significance of Earth’s density in planetary science?
A: The Earth’s density helps in understanding its internal structure, composition, and gravitational effects on surrounding celestial bodies.
FAQs on Mass and Density of Earth
Q1: What is the heaviest layer of the Earth?
A: The inner core is the heaviest and densest layer, primarily composed of iron and nickel.
Q2: How does Earth’s density compare to other planets?
A: Earth has the highest density among the terrestrial planets (Mercury, Venus, Earth, and Mars).
Q3: Can the density of Earth change over time?
A: Yes, due to geological processes like plate tectonics, volcanic activities, and core cooling, slight changes in density may occur.
Q4: How does Earth’s mass affect gravity?
A: Earth’s mass determines the gravitational pull, which influences atmospheric retention, ocean tides, and planetary motion.
Multiple-Choice Questions (MCQs) with Answers
Q1: What is the approximate mass of the Earth?
A) 6.972 × 10²⁴ kg B) 5.972 × 10²⁴ kg C) 4.972 × 10²⁴ kg D) 7.972 × 10²⁴ kg
✅ Answer: B) 5.972 × 10²⁴ kg Explanation: The mass of the Earth has been calculated based on gravitational laws and astronomical observations.
Q2: Which layer of the Earth has the highest density?
A) Crust B) Mantle C) Outer Core D) Inner Core
✅ Answer: D) Inner Core Explanation: The inner core, composed mainly of iron and nickel, has the highest density among all layers.
Q3: Which formula is used to determine the mass of the Earth?
A) F = ma B) M = gR²/G C) P = m/V D) KE = ½mv²
✅ Answer: B) M = gR²/G Explanation: This formula is derived from Newton’s law of gravitation and helps in calculating Earth’s mass.
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Conclusion
Understanding the mass and density of Earth is crucial for gravitational studies, geophysics, and planetary science. For detailed notes, solved examples, and practice questions, buy the complete study material at Anand Technical Publishers.
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