Question
Download Solution PDFWhat is the ratio of the original gravitational force to the new gravitational force when the distance between the masses changes to twice the original distance and the masses are doubled?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is 1 : 1.
Key Points
- Gravitational force between two masses is given by Newton's law of gravitation: F = G * (m1 * m2) / r², where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them.
- If the distance between the two masses is doubled, the gravitational force becomes (1/2² = 1/4) of the original force.
- If both masses are doubled, the product of the masses becomes (2 * 2 = 4) times the original value.
- The combined effect of doubling the masses and doubling the distance results in a net gravitational force of (4 / 4 = 1) compared to the original.
- Thus, the ratio of the original gravitational force to the new gravitational force is 1 : 1.
Additional Information
- Newton's Law of Universal Gravitation
- This law states that every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
- The mathematical expression is: F = G * (m1 * m2) / r², where G is the universal gravitational constant with a value of approximately 6.674 × 10⁻¹¹ N·m²/kg².
- Gravitational Constant (G)
- It is a fundamental constant in physics that quantifies the strength of the gravitational force.
- G is essential in calculating the gravitational force and is the same everywhere in the universe.
- Inverse-Square Law
- The gravitational force follows the inverse-square law, meaning the force decreases with the square of the distance.
- If the distance between two objects doubles, the gravitational force becomes one-fourth of its original value.
- Effect of Mass on Gravitational Force
- Gravitational force is directly proportional to the product of the masses involved.
- If either mass increases, the gravitational force increases proportionally.
Last updated on Apr 24, 2025
-> The AAI Junior Assistant Response Sheet 2025 has been out on the official portal for the written examination.
-> AAI has released 168 vacancies for Western Region. Candidates had applied online from 25th February to 24th March 2025.
-> A total number of 152 Vacancies have been announced for the post of Junior Assistant (Fire Service) for Northern Region.
-> Eligible candidates can apply from 4th February 2025 to 5th March 2025.
-> Candidates who have completed 10th with Diploma or 12th Standard are eligible for this post.
-> The selection process includes a Computer Based Test, Document Verification, Medical Examination (Physical Measurement Test), Driving Test and a Physical Endurance Test.
-> Prepare for the exam with AAI Junior Assistant Previous year papers.