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Four planets A, B, C, and D made up of the same material have a radius of r/2, r, 2r, and 4r respectively. The order of the planets in increasing order of the acceleration due to gravity (on their surface) is:
- a)D, C, B, A
- b)B, C, D, A
- c)A, C, B, D
- d)A, B, C, D
Correct answer is option 'D'. Can you explain this answer?
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Four planets A, B, C, and D made up of the same material have a radius...
The acceleration due to gravity on the surface of a planet depends on the mass and radius of the planet. The formula for acceleration due to gravity on the surface of a planet is:
g = G * M / R^2
where: g = acceleration due to gravity G = gravitational constant M = mass of the planet R = radius of the planet
Since all the planets are made up of the same material, we can assume that they have the same density. Therefore, the mass of the planets is proportional to their volume, which is proportional to the cube of their radius. So we can write:
M ∝ R^3
Substituting this in the formula for acceleration due to gravity, we get:
g = G * (R^3) / R^2 = G * R
So the acceleration due to gravity is directly proportional to the radius of the planet.
Therefore, the order of the planets in increasing order of acceleration due to gravity on their surface is:
A < B < C < D
Since the radius of planet A is r/2, its acceleration due to gravity is (1/2)Gr. The radius of planet B is r, so its acceleration due to gravity is Gr. The radius of planet C is 2r, so its acceleration due to gravity is 2Gr. The radius of planet D is 4r, so its acceleration due to gravity is 4G*r.
So the correct order is: A, B, C, D.
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Four planets A, B, C, and D made up of the same material have a radius...
Dekhh bhai acceleration dueto gravity is directly proportional to radius of planet soo as u increase radius more will be the g of planet
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Four planets A, B, C, and D made up of the same material have a radius...
To determine the order of the planets in increasing order of the acceleration due to gravity on their surface, we need to compare their gravitational forces. The gravitational force between two objects can be calculated using the equation:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
We can simplify the equation by assuming that the mass of the object experiencing the gravitational force (m2) is equal in all cases. This allows us to compare the forces based on the ratios of their masses (m1/m2) and distances (r^2).
Let's analyze the gravitational forces on each planet:
Planet A:
The radius of planet A is r/2. So, the distance between the centers of two objects is (r + r/2) = (3r/2). The ratio of masses is (m1/m2) = 1.
The gravitational force on planet A can be calculated as F_A = (G * m2) / (3r/2)^2.
Planet B:
The radius of planet B is r. So, the distance between the centers of two objects is (r + r) = 2r. The ratio of masses is (m1/m2) = 1.
The gravitational force on planet B can be calculated as F_B = (G * m2) / (2r)^2.
Planet C:
The radius of planet C is 2r. So, the distance between the centers of two objects is (r + 2r) = 3r. The ratio of masses is (m1/m2) = 1.
The gravitational force on planet C can be calculated as F_C = (G * m2) / (3r)^2.
Planet D:
The radius of planet D is 4r. So, the distance between the centers of two objects is (r + 4r) = 5r. The ratio of masses is (m1/m2) = 1.
The gravitational force on planet D can be calculated as F_D = (G * m2) / (5r)^2.
Comparing the forces, we can see that:
F_A = (G * m2) / (3r/2)^2
F_B = (G * m2) / (2r)^2
F_C = (G * m2) / (3r)^2
F_D = (G * m2) / (5r)^2
Since the denominator of the force equation is squared, the higher the value of r, the smaller the force will be. Therefore, the order of the planets in increasing order of the acceleration due to gravity is:
A, B, C, D
Hence, the correct answer is option D.
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
We can simplify the equation by assuming that the mass of the object experiencing the gravitational force (m2) is equal in all cases. This allows us to compare the forces based on the ratios of their masses (m1/m2) and distances (r^2).
Let's analyze the gravitational forces on each planet:
Planet A:
The radius of planet A is r/2. So, the distance between the centers of two objects is (r + r/2) = (3r/2). The ratio of masses is (m1/m2) = 1.
The gravitational force on planet A can be calculated as F_A = (G * m2) / (3r/2)^2.
Planet B:
The radius of planet B is r. So, the distance between the centers of two objects is (r + r) = 2r. The ratio of masses is (m1/m2) = 1.
The gravitational force on planet B can be calculated as F_B = (G * m2) / (2r)^2.
Planet C:
The radius of planet C is 2r. So, the distance between the centers of two objects is (r + 2r) = 3r. The ratio of masses is (m1/m2) = 1.
The gravitational force on planet C can be calculated as F_C = (G * m2) / (3r)^2.
Planet D:
The radius of planet D is 4r. So, the distance between the centers of two objects is (r + 4r) = 5r. The ratio of masses is (m1/m2) = 1.
The gravitational force on planet D can be calculated as F_D = (G * m2) / (5r)^2.
Comparing the forces, we can see that:
F_A = (G * m2) / (3r/2)^2
F_B = (G * m2) / (2r)^2
F_C = (G * m2) / (3r)^2
F_D = (G * m2) / (5r)^2
Since the denominator of the force equation is squared, the higher the value of r, the smaller the force will be. Therefore, the order of the planets in increasing order of the acceleration due to gravity is:
A, B, C, D
Hence, the correct answer is option D.
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Four planets A, B, C, and D made up of the same material have a radius of r/2, r, 2r, and 4r respectively.The order of the planets in increasing order of the acceleration due to gravity (on their surface) is:a)D, C, B, Ab)B, C, D, Ac)A, C, B, Dd)A, B, C, DCorrect answer is option 'D'. Can you explain this answer?
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Four planets A, B, C, and D made up of the same material have a radius of r/2, r, 2r, and 4r respectively.The order of the planets in increasing order of the acceleration due to gravity (on their surface) is:a)D, C, B, Ab)B, C, D, Ac)A, C, B, Dd)A, B, C, DCorrect answer is option 'D'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Four planets A, B, C, and D made up of the same material have a radius of r/2, r, 2r, and 4r respectively.The order of the planets in increasing order of the acceleration due to gravity (on their surface) is:a)D, C, B, Ab)B, C, D, Ac)A, C, B, Dd)A, B, C, DCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four planets A, B, C, and D made up of the same material have a radius of r/2, r, 2r, and 4r respectively.The order of the planets in increasing order of the acceleration due to gravity (on their surface) is:a)D, C, B, Ab)B, C, D, Ac)A, C, B, Dd)A, B, C, DCorrect answer is option 'D'. Can you explain this answer?.
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