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

Answer:

B) 2.18 m/s²

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

$g=\frac{GM}{R^{2}}$

$9.8 =\frac{GM}{R^{2}}$                               eq-1

g' = new acceleration due to gravity of earth

New acceleration due to gravity of earth is given as

$g' =\frac{GM'}{R'^{2}}$

$g' =\frac{G(2M)}{(3R)^{2}}$

$g'=\left ( \frac{2}{9} \right )\frac{GM}{R^{2}}$

Using eq-1

$g'=\left ( \frac{2}{9} \right )(9.8)$

g' = 2.18 m/s²