Respuesta :
Answer:
The same as the escape velocity of asteorid A (50m/s)
Explanation:
The escape velocity is described as follows:
[tex]v=\sqrt{\frac{2GM}{R}}[/tex]
where [tex]G[/tex] is the universal gravitational constant, [tex]M[/tex] is the mass of the asteroid and [tex]R[/tex] is the radius
and since the scape velocity is 50m/s:
[tex]50m/s=\sqrt{\frac{2GM}{R}}[/tex]
Now, if the astroid B has twice mass and twice the radius, we have that tha mass is: [tex]2M[/tex]
and the radius is: [tex]2R[/tex]
inserting these values into the formula for escape velocity:
[tex]v=\sqrt{\frac{2G(2M)}{2R} } =\sqrt{\frac{4GM}{2R} } =\sqrt{\frac{2GM}{R} }[/tex]
and we have found that [tex]50m/s=\sqrt{\frac{2GM}{R}}[/tex], so the two asteroids have the same escape velocity.
We found that the expression for escape velocity remains the same as for asteroid A, this because both quantities (radius and mass) doubled, so it does not affect the equation.
The answer is
Asteroid B would have an escape velocity the same as the escape velocity of asteroid A
Escape velocity is the minimum velocity required to escape. The velocity of both the asteroids is the same which is equal to 50 m/s.
What is escape velocity?
Escape velocity is the minimum velocity of a non-propelled(Free) object needed to escape from the influence of gravitation. It is given by the formula,
[tex]v_e= \sqrt {\dfrac {2GM}{r}}[/tex]
where
[tex]v_e[/tex] is the escape velocity
G is the universal gravitational constant
M is the mass of the body
r is the distance from the center of the mass
We know the formula for the escape velocity, therefore, we will find the velocity of asteroids A and B,
Escape Velocity of Asteroid A,
[tex]v_e= \sqrt {\dfrac {2GM}{r}}[/tex]
Given to us for the asteroid A,
[tex]v_e[/tex] = 50 m/s
[tex]50= \sqrt {\dfrac {2GM}{r}}\\\\2500 = \dfrac {2GM}{r}\\\\\dfrac {M}{r} = \dfrac {2500}{2G}\\\\\dfrac {M}{r} = \dfrac {1250}{G}[/tex]
Now, we know the ratio of weight and the radius, therefore, the escape velocity of asteroid B,
[tex]v_e= \sqrt {\dfrac {2GM}{r}}[/tex]
Given to us for the asteroid B,
Mass of B = Twice the mass of A,
The radius of B = Twice the radius of A,
[tex]v_e= \sqrt {\dfrac {2G(2M)}{(2r)}}\\\\v_e= \sqrt {\dfrac {2GM}{r}}\\\\v_e= \sqrt {\dfrac {2G \times 1250}{G}}\\\\v_e = 50\rm\ m/s[/tex]
Hence, the velocity of both the asteroids is the same which is equal to 50 m/s.
Learn more about Escape Velocity:
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