Select the correct answer.
Object A attracts object B with a gravitational force of 10 newtons from a given distance. If the distance between the two objects is doubled, what is the new force of attraction between them?
A. 2.5 newtons
B. 5 newtons
C. 20 newtons
D. 100 newtons
Answer (1)
The gravitational force is inversely proportional to the square of the distance: F = d 2 k .
When the distance is doubled ( d 2 = 2 d 1 ), the new force becomes F 2 = 4 F 1 .
Given the initial force F 1 = 10 N, the new force is F 2 = 4 10 = 2.5 N.
The new force of attraction between the objects is 2.5 newtons .
Explanation
Understanding the Problem We are given that the gravitational force between two objects is 10 N at a certain distance. We need to find the new force when the distance between the objects is doubled. The gravitational force is inversely proportional to the square of the distance between the objects.
Setting up the Equations Let F 1 be the initial force and d 1 be the initial distance. Let F 2 be the new force and d 2 be the new distance. We know that F 1 = 10 N and d 2 = 2 d 1 . The gravitational force is given by the formula: F = d 2 k where k is a constant of proportionality.
Relating the Initial and New Forces We have F 1 = d 1 2 k and F 2 = d 2 2 k . Since d 2 = 2 d 1 , we can write: F 2 = ( 2 d 1 ) 2 k = 4 d 1 2 k = 4 1 ⋅ d 1 2 k = 4 1 F 1
Calculating the New Force Now, substitute the given value of F 1 = 10 N into the equation: F 2 = 4 1 ( 10 ) = 2.5 N Therefore, the new force of attraction between the objects is 2.5 N.
Examples
Gravitational force is a fundamental concept in physics, governing the interactions between objects with mass. Understanding how gravitational force changes with distance is crucial in various real-world applications. For example, when planning satellite orbits, engineers must consider how the gravitational pull of the Earth affects the satellite's trajectory. If a satellite's distance from Earth is doubled, the gravitational force acting on it decreases by a factor of four, which must be accounted for to maintain the desired orbit. This principle also applies to understanding the motion of planets around stars and the structure of galaxies.
