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A solid sphere of uniform density has a mass of 4.0×104 kg and a radius of 2.5 m. What is the gravitational force due to the sphere on a particle of mass 1.0 kg located at a distance of 3.00 m from the center of the sphere?

Answer 1

#2.96xx10^{-7} "N"#

We can compute the gravitational attraction as if the solid sphere were a point mass with all of the mass concentrated at its center by applying Newton's Shell Theorem.

#F = frac{GMm}{R^2}#

#= frac{(6.67xx10^{-11} "Nm"^2"kg"^{-2})(4.0xx10^4 "kg")(1.0 "kg")}{(3.00 "m")^2}#

# = 2.96xx10^{-7} "N"#

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Answer 2

John Alexander

The gravitational force due to the sphere on a particle of mass 1.0 kg located at a distance of 3.00 m from the center of the sphere is approximately 0.0312 Newtons.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.