Two objects are attracted to each other by a gravitational force F. If the distance between the objects is doubled, what is the new gravitational force between the objects in terms of F?

Question

BlackTom AI · Accepted Answer

Let's lay out the situation step by step.

- The gravitational force between two masses follows the inverse-square law: F ∝ 1/r^2. Therefore, if the distance r is doubled, the force becomes F' = F × (1/2)^2 = F/4.

- This means the new force is one quarter of the original force, regardless of the actual numeric value of F, as long as F refers to the force at the initial distance.

- Now examine the given answer choices:
  - Option a: 1/9 N. This would imply a reduction by a factor of 9, which is not consistent with the 1/r^2 relationship when r is doubled. 
  - Option b: 4 F. This would imply the force increases by a factor of 4, opposite to what the inverse-square law predicts for an increased distance. 
  - Option c: 1/4 N. This corresponds to F' = F/4. If the original force F were 1 N, then F' would be 1/4 N; and the relationship F' = F/4 holds generally for doubling r. 
  - Option d: 16 F. This would imply a massive increase, which again contradicts the 1/r^2 decline when r doubles. 
  - Option e: 9 F. This is another incorrect scaling and does not follow the inverse-square law for r → 2r.

- Conceptually, the key idea is that doubling the separation reduces the gravitational pull by a factor of four, since the force falls with the square of the distance. The numeric value given in the correct option matches the general relation F' = F/4 when the original force is F.

Two objects are attracted to each other by a gravitational force F. If the distance between the objects is doubled, what is the new gravitational force between the objects in terms of F?

View Explanation

Log in for full answers

Similar Questions

What is the force of gravity acting on an astronaut of mass 76.5 kg on a planet of mass 2.8 × 1024 kg and radius 4000 km? Give your answer to the nearest whole number. G is 6.67 × 10-11 in SI units.

A ball is thrown vertically upwards, reaches its highest point, then drops down to the ground, bounces once,reaches a height of 1.2 m, then falls again and finally rests on the grass. At which one or more times is the gravitational force on the ball zero?

A rock is thrown from a cliff and lands in a river below. When the rock is at position X and taking into account the influence of air resistance, which of the following describes the direction of the gravitational force on the rock?

Recall that gravity applies a constant downwards acceleration of 9.8m/sAt rest, what is the approximate ground reaction force applied to a person weighing 62kg?

Compared to its weight on Earth, a 32.5-kg object on the Moon (gravity on moon = 1.63m/s2) will weigh

If an object at the surface of the Earth has a weight W, what would be the weight of the object if it was transported to the surface of a planet that is one-sixth the mass of Earth and has a radius one third that of Earth?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler