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 force on a 1 kg mass at the surface?

Options:

Correct Answer: 9.8 N

Solution:

Using F = G * (m1 * m2) / r^2, F = (6.67 x 10^-11) * (6 x 10^24 * 1) / (6.4 x 10^6)^2 = 9.8 N.

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 force on a 1 kg mass at the surface?

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 force on a 1 kg mass at the surface?

Step 1: Identify the values needed for the formula F = G * (m1 * m2) / r^2. Here, m1 is the mass of the Earth (6 x 10^24 kg), m2 is the mass of the object (1 kg), G is the gravitational constant (6.67 x 10^-11 N m^2/kg^2), and r is the radius of the Earth (6.4 x 10^6 m).
Step 2: Plug the values into the formula: F = (6.67 x 10^-11) * (6 x 10^24 * 1) / (6.4 x 10^6)^2.
Step 3: Calculate the denominator (r^2): (6.4 x 10^6)^2 = 4.096 x 10^13 m^2.
Step 4: Calculate the numerator (G * (m1 * m2)): (6.67 x 10^-11) * (6 x 10^24 * 1) = 4.002 x 10^14 N m^2/kg.
Step 5: Divide the numerator by the denominator to find F: F = (4.002 x 10^14) / (4.096 x 10^13) = 9.8 N.

Gravitational Force Calculation – The question tests the ability to apply Newton's law of universal gravitation to calculate the gravitational force acting on a mass at the surface of the Earth.
Use of Constants – It assesses the understanding of the gravitational constant (G) and its application in the formula.
Unit Consistency – The question requires attention to units, ensuring that mass is in kilograms and distance in meters.