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A mass m is split into two parts m and M-m these two masses are then separated by a distance D. if the gravitational force btw the part is maximum then the ratio of masses is?
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A mass m is split into two parts m and M-m these two masses are then s...
Understanding the Problem
When a mass m is split into two parts, denoted as m and M-m, and separated by a distance D, we want to determine the mass ratio that maximizes the gravitational force between them.
The Gravitational Force Formula
The gravitational force F between two masses is given by:
- F = G * (m * (M-m)) / D^2
Where:
- G = gravitational constant
- m and M-m = the two masses
- D = distance separating the masses
Maximizing the Gravitational Force
To find the mass ratio that maximizes the gravitational force, we can analyze the function:
- F = G * (m * (M-m))
This expression represents a quadratic function in terms of m.
Finding the Maximum
To maximize this function, we can use the concept of differentiation:
- The maximum value occurs when the derivative of F with respect to m is zero.
Setting the derivative to zero gives:
- M - 2m = 0
From this, we find:
- m = M/2
Thus, the two masses are equal.
Ratio of Masses
The ratio of the two masses is:
- m : (M-m) = (M/2) : (M/2) = 1 : 1
Conclusion
When the gravitational force between the two parts of the mass is maximized, the ratio of the two masses is 1:1. This signifies that splitting the original mass into two equal parts results in the strongest gravitational attraction between them.
When a mass m is split into two parts, denoted as m and M-m, and separated by a distance D, we want to determine the mass ratio that maximizes the gravitational force between them.
The Gravitational Force Formula
The gravitational force F between two masses is given by:
- F = G * (m * (M-m)) / D^2
Where:
- G = gravitational constant
- m and M-m = the two masses
- D = distance separating the masses
Maximizing the Gravitational Force
To find the mass ratio that maximizes the gravitational force, we can analyze the function:
- F = G * (m * (M-m))
This expression represents a quadratic function in terms of m.
Finding the Maximum
To maximize this function, we can use the concept of differentiation:
- The maximum value occurs when the derivative of F with respect to m is zero.
Setting the derivative to zero gives:
- M - 2m = 0
From this, we find:
- m = M/2
Thus, the two masses are equal.
Ratio of Masses
The ratio of the two masses is:
- m : (M-m) = (M/2) : (M/2) = 1 : 1
Conclusion
When the gravitational force between the two parts of the mass is maximized, the ratio of the two masses is 1:1. This signifies that splitting the original mass into two equal parts results in the strongest gravitational attraction between them.
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A mass m is split into two parts m and M-m these two masses are then separated by a distance D. if the gravitational force btw the part is maximum then the ratio of masses is?
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A mass m is split into two parts m and M-m these two masses are then separated by a distance D. if the gravitational force btw the part is maximum then the ratio of masses is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A mass m is split into two parts m and M-m these two masses are then separated by a distance D. if the gravitational force btw the part is maximum then the ratio of masses is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass m is split into two parts m and M-m these two masses are then separated by a distance D. if the gravitational force btw the part is maximum then the ratio of masses is?.
A mass m is split into two parts m and M-m these two masses are then separated by a distance D. if the gravitational force btw the part is maximum then the ratio of masses is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A mass m is split into two parts m and M-m these two masses are then separated by a distance D. if the gravitational force btw the part is maximum then the ratio of masses is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass m is split into two parts m and M-m these two masses are then separated by a distance D. if the gravitational force btw the part is maximum then the ratio of masses is?.
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