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The gravitational force between two objects is F. If masses of both the objects are halved and
the distance between them is also halved, then the gravitational force would become?
the distance between them is also halved, then the gravitational force would become?
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The gravitational force between two objects is F. If masses of both th...
Understanding Gravitational Force
The gravitational force (F) between two masses (m1 and m2) separated by a distance (r) is given by Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where G is the gravitational constant.
New Masses and Distance
In this scenario:
- The masses of both objects are halved:
- New m1 = m1 / 2
- New m2 = m2 / 2
- The distance between them is also halved:
- New r = r / 2
Substituting the New Values
Now, substituting the new values into the gravitational force formula:
- New F = G * ((m1 / 2) * (m2 / 2)) / (r / 2)^2
Calculating the New Gravitational Force
Let's break this down:
- The numerator becomes:
- (m1 * m2) / 4
- The denominator becomes:
- (r^2 / 4)
Thus, the new formula becomes:
New F = G * (m1 * m2 / 4) / (r^2 / 4)
Final Simplification
When we simplify this, we get:
New F = G * (m1 * m2) / r^2
This shows that the gravitational force remains unchanged:
Conclusion
- The new gravitational force is equal to the original force (F).
- Result: The force remains F, even with halved masses and halved distance.
This illustrates that while individual components change, their relationship maintains the overall force constant.
The gravitational force (F) between two masses (m1 and m2) separated by a distance (r) is given by Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where G is the gravitational constant.
New Masses and Distance
In this scenario:
- The masses of both objects are halved:
- New m1 = m1 / 2
- New m2 = m2 / 2
- The distance between them is also halved:
- New r = r / 2
Substituting the New Values
Now, substituting the new values into the gravitational force formula:
- New F = G * ((m1 / 2) * (m2 / 2)) / (r / 2)^2
Calculating the New Gravitational Force
Let's break this down:
- The numerator becomes:
- (m1 * m2) / 4
- The denominator becomes:
- (r^2 / 4)
Thus, the new formula becomes:
New F = G * (m1 * m2 / 4) / (r^2 / 4)
Final Simplification
When we simplify this, we get:
New F = G * (m1 * m2) / r^2
This shows that the gravitational force remains unchanged:
Conclusion
- The new gravitational force is equal to the original force (F).
- Result: The force remains F, even with halved masses and halved distance.
This illustrates that while individual components change, their relationship maintains the overall force constant.
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The gravitational force between two objects is F. If masses of both the objects are halved and the distance between them is also halved, then the gravitational force would become?
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The gravitational force between two objects is F. If masses of both the objects are halved and the distance between them is also halved, then the gravitational force would become? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The gravitational force between two objects is F. If masses of both the objects are halved and the distance between them is also halved, then the gravitational force would become? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The gravitational force between two objects is F. If masses of both the objects are halved and the distance between them is also halved, then the gravitational force would become?.
The gravitational force between two objects is F. If masses of both the objects are halved and the distance between them is also halved, then the gravitational force would become? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The gravitational force between two objects is F. If masses of both the objects are halved and the distance between them is also halved, then the gravitational force would become? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The gravitational force between two objects is F. If masses of both the objects are halved and the distance between them is also halved, then the gravitational force would become?.
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