If the mass of the Earth is 6 × 10^24 kg and its radius is 6.4 × 10^6 m, what is

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Question: If the mass of the Earth is 6 × 10^24 kg and its radius is 6.4 × 10^6 m, what is the acceleration due to gravity at its surface?

Options:

Correct Answer: 9.81 m/s²

Solution:

g = G * M / R² = (6.67 × 10^-11) * (6 × 10^24) / (6.4 × 10^6)² = 9.81 m/s²

If the mass of the Earth is 6 × 10^24 kg and its radius is 6.4 × 10^6 m, what is the acceleration due to gravity at its surface?

If the mass of the Earth is 6 × 10^24 kg and its radius is 6.4 × 10^6 m, what is the acceleration due to gravity at its surface?

Step 1: Identify the formula for acceleration due to gravity, which is g = G * M / R².
Step 2: Note the values needed for the calculation: G (gravitational constant) = 6.67 × 10^-11 m³/(kg·s²), M (mass of the Earth) = 6 × 10^24 kg, and R (radius of the Earth) = 6.4 × 10^6 m.
Step 3: Substitute the values into the formula: g = (6.67 × 10^-11) * (6 × 10^24) / (6.4 × 10^6)².
Step 4: Calculate the denominator (R²): (6.4 × 10^6)² = 4.096 × 10^13 m².
Step 5: Calculate the numerator: (6.67 × 10^-11) * (6 × 10^24) = 4.002 × 10^14 m³/(kg·s²).
Step 6: Divide the numerator by the denominator: g = 4.002 × 10^14 / 4.096 × 10^13.
Step 7: Perform the division to find g: g ≈ 9.81 m/s².

Gravitational Acceleration – The calculation of gravitational acceleration using the formula g = G * M / R², where G is the gravitational constant, M is the mass of the Earth, and R is the radius of the Earth.
Units and Constants – Understanding the significance of units (kg, m, s²) and the gravitational constant (G) in the context of the formula.