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Chapter 8: Problem 8

If the distance between two point particles is doubled, then the gravitational force between them (A) decreases by a factor of 4 (B) decreases by a factor of 2 (C) increases by a factor of 2 (D) increases by a factor of 4

Short Answer

Expert verified
(A) decreases by a factor of 4

Step by step solution

01

Understand Newton's Law of Universal Gravitation

The formula for gravitational force (\( F \)) is given by Newton's law of universal gravitation: \( F = G * \frac{m1 * m2}{r^2} \), where \( G \)is the gravitational constant, \( m1 \) and \( m2 \)are the masses of two bodies and \( r \)is the distance between the centers of two bodies.
02

Analyze the effect of doubling the distance

We have been asked about the effect on gravitational force (\( F \)) if the distance (\( r \)) is doubled. Replacing \( r \)with \( 2r \)in the formula, we get \( F' = G * \frac{m1 * m2}{(2r)^2} = G * \frac{m1 * m2}{4r^2} \). This new force (\( F' \)) is one-fourth the original force (\( F \)).
03

Choose the correct answer

From the derivation in Step-2 we can conclude that if the distance between two point particles is doubled, the gravitational force between them decreases by a factor of 4. So our correct answer is (A)

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Most popular questions from this chapter

A moon of Jupiter has a nearly circular orbit of radius \(R\) and an orbit period of \(T\). Which of the following expressions gives the mass of Jupiter? (A) \(\frac{4 \pi^{2} R}{T^{2}}\) (B) \(\frac{2 \pi R^{3}}{\left(G T^{2}\right)}\) (C) \(\frac{4 \pi R^{2}}{\left(G T^{2}\right)}\) (D) \(\frac{4 \pi^{2} R^{3}}{\left(G T^{2}\right)}\)

At the surface of Earth, an object of mass \(m\) has weight \(w\). If this object is transported to an altitude that is twice the radius of Earth, then at the new location, (A) its mass is \(m\) and its weight is \(w / 2\) (B) its mass is \(m / 2\) and its weight is \(w / 4\) (C) its mass is \(m\) and its weight is \(w / 4\) (D) its mass is \(m\) and its weight is \(w / 9\)

An object moves at constant speed in a circular path. Which of the following statements are true? Select two answers. (A) The velocity is changing. (B) The velocity is constant. (C) The magnitude of acceleration is constant. (D) The magnitude of acceleration is changing.

A \(60 \mathrm{~cm}\) rope is tied to the handle of a bucket which is then whirled in a vertical circle. The mass of the bucket is \(3 \mathrm{~kg}\). At the lowest point in its path, the tension in the rope is \(50 \mathrm{~N}\). What is the speed of the bucket? (A) \(1 \mathrm{~m} / \mathrm{s}\) (B) \(2 \mathrm{~m} / \mathrm{s}\) (C) \(3 \mathrm{~m} / \mathrm{s}\) (D) \(4 \mathrm{~m} / \mathrm{s}\)

A \(60 \mathrm{~cm}\) rope is tied to the handle of a bucket which is then whirled in a vertical circle. The mass of the bucket is \(3 \mathrm{~kg}\). What is the critical speed below which the rope would become slack when the bucket reaches the highest point in the circle? (A) \(0.6 \mathrm{~m} / \mathrm{s}\) (B) \(1.8 \mathrm{~m} / \mathrm{s}\) (C) \(2.4 \mathrm{~m} / \mathrm{s}\) (D) \(4.8 \mathrm{~m} / \mathrm{s}\)
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