Answer:
The mass of the planet is 55 times the mass of earth.
Explanation:
From the inverse-square gravitation law,
F = (GMm/r²)
If the weight of a body (the force with which the earth attracts a body to its centre) is to be calculated,
F = mg
m = mass of the body,
g = acceleration due to gravity
mg = (GMm/r²)
G = Gravitational constant
M = mass of the earth
m = mass of body
r = distance between the body and the centre of the earth = radius of the earth
The acceleration due to gravity is given by
g = (GM/r²)
Making the mass of the earth, the subject of formula
M = (gr²/G) (eqn 1)
So, the planet described,
Let the acceleration due to gravity on the planet be g₁
Mass of the planet be M₁
Radius of the planet be r₁
g₁ = 2.2g
r₁ = 5r
M₁ = ?
Note that the gravitational constant is the same for both planets.
So, we can write a similar expression for the planet's acceleration due to gravity
g₁ = (GM₁/r₁²)
Substituting all the parameters known in terms of their corresponding earth values
2.2g = [GM₁/(5r)²]
2.2g = [GM₁/25r²]
M₁ = (55gr²/G)
Recall the expression for the mass of the earth
M = (gr²/G)
M₁ = 55 M
The mass of the planet, in terms of Earth masses = 55M
The mass of the planet is 55 times the planet of earth.
Hope this Helps!!!
