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

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Question: If the mass of the Earth is 6 x 10^24 kg and the radius is 6.4 x 10^6 m, what is the gravitational acceleration at the surface of the Earth?

Options:

  1. 9.8 m/s²
  2. 10 m/s²
  3. 9.81 m/s²
  4. 11 m/s²

Correct Answer: 9.8 m/s²

Solution: 

Using g = G * M / R², where G = 6.67 x 10^-11 N m²/kg², M = 6 x 10^24 kg, and R = 6.4 x 10^6 m, we find g ≈ 9.8 m/s².

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

Practice Questions

Q1
If the mass of the Earth is 6 x 10^24 kg and the radius is 6.4 x 10^6 m, what is the gravitational acceleration at the surface of the Earth?
  1. 9.8 m/s²
  2. 10 m/s²
  3. 9.81 m/s²
  4. 11 m/s²

Questions & Step-by-Step Solutions

If the mass of the Earth is 6 x 10^24 kg and the radius is 6.4 x 10^6 m, what is the gravitational acceleration at the surface of the Earth?
  • Step 1: Identify the formula for gravitational acceleration, which is g = G * M / R².
  • Step 2: Write down the values you have: G = 6.67 x 10^-11 N m²/kg², M = 6 x 10^24 kg, and R = 6.4 x 10^6 m.
  • Step 3: Calculate R² (the radius squared). R² = (6.4 x 10^6 m) * (6.4 x 10^6 m).
  • Step 4: Multiply the mass (M) by the gravitational constant (G). Calculate G * M = (6.67 x 10^-11 N m²/kg²) * (6 x 10^24 kg).
  • Step 5: Divide the result from Step 4 by the result from Step 3 to find g. g = (G * M) / R².
  • Step 6: Calculate the final value of g, which should be approximately 9.8 m/s².
  • Gravitational Acceleration – Understanding the formula for gravitational acceleration and how to apply it using mass and radius.
  • Units and Constants – Knowledge of the gravitational constant (G) and its units, as well as the conversion of scientific notation.
  • Physics of Gravity – Application of Newton's law of universal gravitation in calculating gravitational force.
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