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A mass M is split into two parts, m and (M-m), which r thn separated by a certain distance. What ratio of m/M maximizes the gravitational force btwn the two parts? (ans is 1/2). plsss expln
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A mass M is split into two parts, m and (M-m), which r thn separated b...
Introduction:
This problem deals with optimizing the gravitational force between two parts of a mass that are separated by a certain distance. The objective is to find the ratio of the two parts that maximizes this force.
Formula:
The gravitational force between two masses is given by the formula:
F = G * (m1 * m2) / r^2
where F is the force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them.
Derivation:
Let the two parts of the mass be m and (M-m), where M is the total mass. The distance between them is r. Then, the gravitational force between them is given by:
F = G * (m * (M-m)) / r^2
We want to maximize this force by finding the value of m/M that maximizes it. To do this, we can take the derivative of F with respect to m and set it to zero:
dF/dm = G * ((M-2m) / r^2) = 0
Solving for m, we get:
m = M/2
Therefore, the ratio of m/M that maximizes the gravitational force between the two parts of the mass is 1/2.
Conclusion:
The optimal ratio of the two parts of the mass that maximizes the gravitational force between them is 1/2. This can be derived by taking the derivative of the force equation with respect to m and setting it to zero.
This problem deals with optimizing the gravitational force between two parts of a mass that are separated by a certain distance. The objective is to find the ratio of the two parts that maximizes this force.
Formula:
The gravitational force between two masses is given by the formula:
F = G * (m1 * m2) / r^2
where F is the force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them.
Derivation:
Let the two parts of the mass be m and (M-m), where M is the total mass. The distance between them is r. Then, the gravitational force between them is given by:
F = G * (m * (M-m)) / r^2
We want to maximize this force by finding the value of m/M that maximizes it. To do this, we can take the derivative of F with respect to m and set it to zero:
dF/dm = G * ((M-2m) / r^2) = 0
Solving for m, we get:
m = M/2
Therefore, the ratio of m/M that maximizes the gravitational force between the two parts of the mass is 1/2.
Conclusion:
The optimal ratio of the two parts of the mass that maximizes the gravitational force between them is 1/2. This can be derived by taking the derivative of the force equation with respect to m and setting it to zero.
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A mass M is split into two parts, m and (M-m), which r thn separated by a certain distance. What ratio of m/M maximizes the gravitational force btwn the two parts? (ans is 1/2). plsss expln
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A mass M is split into two parts, m and (M-m), which r thn separated by a certain distance. What ratio of m/M maximizes the gravitational force btwn the two parts? (ans is 1/2). plsss expln for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A mass M is split into two parts, m and (M-m), which r thn separated by a certain distance. What ratio of m/M maximizes the gravitational force btwn the two parts? (ans is 1/2). plsss expln covers all topics & solutions for NEET 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), which r thn separated by a certain distance. What ratio of m/M maximizes the gravitational force btwn the two parts? (ans is 1/2). plsss expln.
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