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What will be the acceleration due to gravity at a planet whose mass is sixteen times the mass of the earth and whose radius is twice that of the earth?
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What will be the acceleration due to gravity at a planet whose mass is...
Understanding Acceleration Due to Gravity
The acceleration due to gravity (g) on a planet can be calculated using the formula:
g = G * M / R²
Where:
- G is the gravitational constant (approximately 6.674 × 10^-11 N(m/kg)²),
- M is the mass of the planet,
- R is the radius of the planet.
Given Values
- Mass of the planet (M) = 16 * Mass of Earth
- Radius of the planet (R) = 2 * Radius of Earth
Calculating Gravity on the New Planet
1. Mass of the Earth (M_E):
- M_E = 5.972 × 10^24 kg
- Therefore, M = 16 * M_E = 16 * 5.972 × 10^24 kg = 9.6352 × 10^25 kg
2. Radius of the Earth (R_E):
- R_E = 6,371 km = 6.371 × 10^6 m
- Therefore, R = 2 * R_E = 2 * 6.371 × 10^6 m = 1.2742 × 10^7 m
3. Substituting in the Gravity Formula:
- g = G * M / R²
- g = (6.674 × 10^-11 N(m/kg)²) * (9.6352 × 10^25 kg) / (1.2742 × 10^7 m)²
Final Calculation
By performing the calculations, you will find:
- g ≈ 10.4 m/s²
Conclusion
The acceleration due to gravity on this new planet is approximately 10.4 m/s². This value is less than Earth's gravity (about 9.81 m/s²) due to the larger radius, despite the higher mass. Thus, the effects of mass and radius on gravity are crucial in understanding planetary dynamics.
The acceleration due to gravity (g) on a planet can be calculated using the formula:
g = G * M / R²
Where:
- G is the gravitational constant (approximately 6.674 × 10^-11 N(m/kg)²),
- M is the mass of the planet,
- R is the radius of the planet.
Given Values
- Mass of the planet (M) = 16 * Mass of Earth
- Radius of the planet (R) = 2 * Radius of Earth
Calculating Gravity on the New Planet
1. Mass of the Earth (M_E):
- M_E = 5.972 × 10^24 kg
- Therefore, M = 16 * M_E = 16 * 5.972 × 10^24 kg = 9.6352 × 10^25 kg
2. Radius of the Earth (R_E):
- R_E = 6,371 km = 6.371 × 10^6 m
- Therefore, R = 2 * R_E = 2 * 6.371 × 10^6 m = 1.2742 × 10^7 m
3. Substituting in the Gravity Formula:
- g = G * M / R²
- g = (6.674 × 10^-11 N(m/kg)²) * (9.6352 × 10^25 kg) / (1.2742 × 10^7 m)²
Final Calculation
By performing the calculations, you will find:
- g ≈ 10.4 m/s²
Conclusion
The acceleration due to gravity on this new planet is approximately 10.4 m/s². This value is less than Earth's gravity (about 9.81 m/s²) due to the larger radius, despite the higher mass. Thus, the effects of mass and radius on gravity are crucial in understanding planetary dynamics.
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What will be the acceleration due to gravity at a planet whose mass is sixteen times the mass of the earth and whose radius is twice that of the earth?
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What will be the acceleration due to gravity at a planet whose mass is sixteen times the mass of the earth and whose radius is twice that of the earth? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about What will be the acceleration due to gravity at a planet whose mass is sixteen times the mass of the earth and whose radius is twice that of the earth? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the acceleration due to gravity at a planet whose mass is sixteen times the mass of the earth and whose radius is twice that of the earth?.
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