D. The acceleration due to gravity at the surface of the moon is 1.6 m/s2. If the radius of the moon is 1.7 x 10 m, calculate the mass of the moon.

Correct question:

The acceleration due to gravity at the surface of the moon is 1.6 m/s2. If the radius

of the moon is 1.74 x 10^6 m, calculate the mass of the moon

M = 7.3 × 10^22

Explanation:

Given the following :

Acceleration due to gravity (g) at surface of the moon = 1.6m/s^2

Radius of the moon (r) = 1.7 × 10^6 m

The acceleration due to gravity of large bodies such as the moon is calculated using the formula :

g = GM / r^2

Where;

g = acceleration due to gravity

G = the universal gravitational constant, G = (6.673 x 10^-11)

M = mass

r = the distance from the center of mass of the body

Therefore, to calculate mass M from the formula :

M = gr^2 / G

Inputting our values :

M = [1.6 × (1.7×10^6)^2] / 6.673 x 10^-11

M = [1.6 × (3.0276×10^12)] / 6.673 x 10^-11

M = (4.84416 × 10^12) / 6.673 × 10^-11

M = 0.7259 × 10^(12+11)

M = 0.7259 × 10^23

M = 7.259 × 10^23

M = 7.3 × 10^22