Multiple Choice
According to Newton's Law of Gravity, what is the magnitude of the net gravitational force exerted on the Sun by a planet of mass m orbiting at a distance r with gravitational constant G?
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8. Centripetal Forces & Gravitation
Newton's Law of Gravity
Multiple Choice
The mass of the moon is 7.36 × 10^22 kg and its distance to the Earth is 3.84 × 10^8 m. What is the gravitational force of the moon on the Earth, given that the gravitational constant G is 6.674 × 10^-11 N(m/kg)^2?
A
6.67 × 10^11 N
B
3.84 × 10^22 N
C
1.98 × 10^20 N
D
7.36 × 10^22 N
Verified step by step guidance1
Identify the formula for gravitational force: The gravitational force between two masses is given by Newton's law of universal gravitation, which is F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the centers of the two masses.
Assign the given values to the variables in the formula: Here, m1 is the mass of the moon (7.36 × 10^22 kg), m2 is the mass of the Earth (which is not given but is approximately 5.97 × 10^24 kg), r is the distance between the Earth and the moon (3.84 × 10^8 m), and G is the gravitational constant (6.674 × 10^-11 N(m/kg)^2).
Substitute the values into the formula: Replace m1, m2, r, and G in the formula F = G * (m1 * m2) / r^2 with the given values. This will give you F = 6.674 × 10^-11 * (7.36 × 10^22 * 5.97 × 10^24) / (3.84 × 10^8)^2.
Simplify the expression: First, calculate the product of the masses (m1 * m2), then calculate the square of the distance (r^2), and finally divide the product of the masses by the square of the distance. Multiply the result by the gravitational constant G.
Interpret the result: The calculated value will give you the gravitational force between the Earth and the moon. Ensure that the units are consistent and the result is in newtons (N).
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