Question

If the radius of the earth was suddenly tripled and its mass doubled, the surface gravitational acceleration would become: A) 9.8 m/s^2

B) 2.18 m/s^2
C) 7.35 m/s^2
D) 14.7 m/s^2
E) 13.1 m/s^2

Answer 1

B) 2.18 m/s²

Step-by-step explanation:

M = Original mass of earth

R = Original radius of earth

g = original acceleration due to gravity of earth = 9.8 m/s²

M' = New mass of earth = 2 M

R' = New radius of earth = 3 R

g = original acceleration due to gravity of earth = 9.8 m/s²

Original acceleration due to gravity of earth is given as

`g=(GM)/(R^(2))`

`9.8 =(GM)/(R^(2))` eq-1

g' = new acceleration due to gravity of earth

New acceleration due to gravity of earth is given as

`g' =(GM')/(R'^(2))`

`g' =(G(2M))/((3R)^(2))`

`g'=\left ( (2)/(9) \right )(GM)/(R^(2))`

Using eq-1

`g'=\left ( (2)/(9) \right )(9.8)`

g' = 2.18 m/s²