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The masses of two planets are in the ratio 1 : 2. Their radii are in the ratio 1 : 2. The acceleration due to gravity on the planets are in the ratio.
- a)1 : 2
- b)2 : 1
- c)3 : 5
- d)5 : 3
Correct answer is option 'A'. Can you explain this answer?
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The masses of two planets are in the ratio 1 : 2. Their radii are in t...
Acc to law of gravitation : mg1=GM1m/R1^2
g1= GM1 / R1^2
( considering that for the first planet variables are placed with 1 and for the second with 2 )
Similarly g2 = G M2/R2^2
As we know that M2 is twice of M1 and R2 is twice of R1
So g2= G2M1/(2R1)^2
g1/g2 = G M1/R1^2 X 4R1^2/G2M1
g1:g2 = 4:2 = 2:1
Most Upvoted Answer
The masses of two planets are in the ratio 1 : 2. Their radii are in t...
Mass and Radius of the Planets:
Let's assume the mass of the first planet is 'm' and its radius is 'r'. Therefore, the mass of the second planet would be 2m and its radius would be 2r.
Gravitational Force:
The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Mathematically, it can be represented as:
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 objects, and r is the distance between them.
Acceleration due to Gravity:
The acceleration due to gravity is the force experienced by a mass due to the gravitational attraction of another mass. It can be calculated by dividing the gravitational force acting on an object by its mass. Mathematically, it can be represented as:
a = F / m
Where a is the acceleration due to gravity, F is the gravitational force, and m is the mass of the object.
Calculating the Acceleration due to Gravity:
Let's calculate the acceleration due to gravity for the first planet:
a1 = G * (m * m1) / r^2
Similarly, for the second planet:
a2 = G * (2m * 2m) / (2r)^2
= G * (4m^2) / (4r^2)
= G * (m^2) / r^2
Comparing the Acceleration due to Gravity:
Now, let's compare the two accelerations:
a1 / a2 = (G * (m * m1) / r^2) / (G * (m^2) / r^2)
= (m * m1) / (m^2)
= m1 / m
Since the masses of the planets are in the ratio 1:2, m1 / m = 1 / 2.
Hence, the ratio of the accelerations due to gravity on the two planets is 1:2, which corresponds to option A.
Let's assume the mass of the first planet is 'm' and its radius is 'r'. Therefore, the mass of the second planet would be 2m and its radius would be 2r.
Gravitational Force:
The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Mathematically, it can be represented as:
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 objects, and r is the distance between them.
Acceleration due to Gravity:
The acceleration due to gravity is the force experienced by a mass due to the gravitational attraction of another mass. It can be calculated by dividing the gravitational force acting on an object by its mass. Mathematically, it can be represented as:
a = F / m
Where a is the acceleration due to gravity, F is the gravitational force, and m is the mass of the object.
Calculating the Acceleration due to Gravity:
Let's calculate the acceleration due to gravity for the first planet:
a1 = G * (m * m1) / r^2
Similarly, for the second planet:
a2 = G * (2m * 2m) / (2r)^2
= G * (4m^2) / (4r^2)
= G * (m^2) / r^2
Comparing the Acceleration due to Gravity:
Now, let's compare the two accelerations:
a1 / a2 = (G * (m * m1) / r^2) / (G * (m^2) / r^2)
= (m * m1) / (m^2)
= m1 / m
Since the masses of the planets are in the ratio 1:2, m1 / m = 1 / 2.
Hence, the ratio of the accelerations due to gravity on the two planets is 1:2, which corresponds to option A.
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The masses of two planets are in the ratio 1 : 2. Their radii are in the ratio 1 : 2. The acceleration due to gravity on the planets are in the ratio.a)1 : 2b)2 : 1c)3 : 5d)5 : 3Correct answer is option 'A'. Can you explain this answer?
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