
Gravitational acceleration on the surface of a planet is , where is the gravitational acceleration on the surface of the earth. The average mass density of the planet is times that of the earth. If the escape speed on the surface of earth is taken to be what will be the escape speed on the surface of this planet?
Answer
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Hint: The gravitational force is defined as the force which acts between two masses. It is always attractive.Escape speed of a moving body is the minimum speed required to escape from the gravitational field of a planet and move into space.We use the relation of gravitational acceleration and escape velocity to obtain the escape velocity on the planet.
Formula used:
Acceleration due to gravity on the surface of a planet is and,the escape velocity from the surface of the planet is
Complete answer:
Acceleration due to gravity is the acceleration of the object due to gravitational force of a planet.
Acceleration due to gravity on a planet of mass and radius is given by relation
where G is the gravitational constant
The escape velocity of an object from the surface of the planet is
Mass density is defined as volumetric mass and given by
where m and V denotes mass and volume of the material respectively.
Assuming a planet to be spherical, its mass density can be given as
Substituting this in (1) and rearranging, we get
Now we substitute this value in (2) and get
Similarly acceleration due to gravity of earth is given by’
Taking ratio of and and substituting the given values; we get
We conclude that escape velocity on the planet is 3 km /s.
Note:
Escape velocity is the minimum speed required to get out from the gravitational field of the planet. Escape velocity is independent of mass of the object. It depends on the radius of the planet and acceleration due to gravitational force of the planet.
Escape velocity on the surface of the earth is 11.2 km/s.
Formula used:
Acceleration due to gravity on the surface of a planet is
Complete answer:
Acceleration due to gravity is the acceleration of the object due to gravitational force of a planet.
Acceleration due to gravity on a planet of mass
The escape velocity of an object from the surface of the planet is
Mass density is defined as volumetric mass and given by
Assuming a planet to be spherical, its mass density can be given as
Substituting this in (1) and rearranging, we get
Now we substitute this value in (2) and get
Similarly acceleration due to gravity of earth is given by’
Taking ratio of
We conclude that escape velocity on the planet is 3 km /s.
Note:
Escape velocity is the minimum speed required to get out from the gravitational field of the planet. Escape velocity is independent of mass of the object. It depends on the radius of the planet and acceleration due to gravitational force of the planet.
Escape velocity on the surface of the earth is 11.2 km/s.
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