Mass of the moon is 7.4x10^22 kg and its radius is 1740km, Calculate the value of acceleration due to gravity on the surface of the moon. *​

The gravitational acceleration in the surface of the moon is 1.63 m/s^2

Explanation:

The gravitational acceleration at a distance R of an object of mass M, is given by:

g = G*M/R^2

Where:

G is the gravitational constant.

G = 6.67*10^(-11) m^3/(kg*s^2)

We could think that all the mass of the moon is at its center, then at the surface of the moon, the distance will be equal to the radius of the moon, thus:

R = 1740km

But we want to work with meters, so remember that:

1km = 1000m

then:

1740km = (1740)*1000m = 1740000m

R =  1740000m

And the mass is just:

M = 7.4x10^22 kg

If we input all that in the gravitational acceleration equation, we get:

g = (6.67*10^(-11) m^3/(kg*s^2))*(7.4x10^22 kg)/( 1740000m)^2

g = 1.63 m/s^2

The gravitational acceleration in the surface of the moon is 1.63 m/s^2