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Two point objects of mass 2x and 3x are separated by a distance r. Keeping the distance fixed, how much mass should be transferred from 3x to 2x, so that gravitational force between them becomes maximum? 1) x/4 2) x/3 3) x/2 4) 2 x/3?
Most Upvoted Answer
Two point objects of mass 2x and 3x are separated by a distance r. Kee...
X/2 so, that both the objects have equal mass for maximum Gravitational force.
Community Answer
Two point objects of mass 2x and 3x are separated by a distance r. Kee...
Solution:
To find the mass that should be transferred from 3x to 2x, we need to analyze the relationship between the gravitational force and the masses.
Gravitational Force:
The gravitational force between two point objects is given by the formula:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2 / kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
Maximizing the Gravitational Force:
To maximize the gravitational force between the two objects, we need to find the mass distribution that maximizes the product m1 * m2.
Let's assume that the mass transferred from 3x to 2x is y.
After the transfer, the masses of the objects become:
Object 1: 2x + y
Object 2: 3x - y
The product of the masses is then:
(2x + y) * (3x - y)
Now, we need to maximize this product by finding the value of y that maximizes it.
Expanding the Product:
(2x + y) * (3x - y) = 6x^2 - 2xy + 3xy - y^2
= 6x^2 + xy - y^2
Maximizing the Product:
To find the maximum value of this product, we can take the derivative with respect to y and set it equal to zero.
d/dy (6x^2 + xy - y^2) = x - 2y = 0
Solving for y, we get:
y = x / 2
Therefore, the mass that should be transferred from 3x to 2x to maximize the gravitational force is x / 2.
Answer:
The correct option is 3) x/2.
By transferring a mass of x/2 from 3x to 2x, the gravitational force between the two objects becomes maximum.
To find the mass that should be transferred from 3x to 2x, we need to analyze the relationship between the gravitational force and the masses.
Gravitational Force:
The gravitational force between two point objects is given by the formula:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2 / kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
Maximizing the Gravitational Force:
To maximize the gravitational force between the two objects, we need to find the mass distribution that maximizes the product m1 * m2.
Let's assume that the mass transferred from 3x to 2x is y.
After the transfer, the masses of the objects become:
Object 1: 2x + y
Object 2: 3x - y
The product of the masses is then:
(2x + y) * (3x - y)
Now, we need to maximize this product by finding the value of y that maximizes it.
Expanding the Product:
(2x + y) * (3x - y) = 6x^2 - 2xy + 3xy - y^2
= 6x^2 + xy - y^2
Maximizing the Product:
To find the maximum value of this product, we can take the derivative with respect to y and set it equal to zero.
d/dy (6x^2 + xy - y^2) = x - 2y = 0
Solving for y, we get:
y = x / 2
Therefore, the mass that should be transferred from 3x to 2x to maximize the gravitational force is x / 2.
Answer:
The correct option is 3) x/2.
By transferring a mass of x/2 from 3x to 2x, the gravitational force between the two objects becomes maximum.
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Two point objects of mass 2x and 3x are separated by a distance r. Keeping the distance fixed, how much mass should be transferred from 3x to 2x, so that gravitational force between them becomes maximum? 1) x/4 2) x/3 3) x/2 4) 2 x/3?
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Two point objects of mass 2x and 3x are separated by a distance r. Keeping the distance fixed, how much mass should be transferred from 3x to 2x, so that gravitational force between them becomes maximum? 1) x/4 2) x/3 3) x/2 4) 2 x/3? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two point objects of mass 2x and 3x are separated by a distance r. Keeping the distance fixed, how much mass should be transferred from 3x to 2x, so that gravitational force between them becomes maximum? 1) x/4 2) x/3 3) x/2 4) 2 x/3? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two point objects of mass 2x and 3x are separated by a distance r. Keeping the distance fixed, how much mass should be transferred from 3x to 2x, so that gravitational force between them becomes maximum? 1) x/4 2) x/3 3) x/2 4) 2 x/3?.
Two point objects of mass 2x and 3x are separated by a distance r. Keeping the distance fixed, how much mass should be transferred from 3x to 2x, so that gravitational force between them becomes maximum? 1) x/4 2) x/3 3) x/2 4) 2 x/3? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two point objects of mass 2x and 3x are separated by a distance r. Keeping the distance fixed, how much mass should be transferred from 3x to 2x, so that gravitational force between them becomes maximum? 1) x/4 2) x/3 3) x/2 4) 2 x/3? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two point objects of mass 2x and 3x are separated by a distance r. Keeping the distance fixed, how much mass should be transferred from 3x to 2x, so that gravitational force between them becomes maximum? 1) x/4 2) x/3 3) x/2 4) 2 x/3?.
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