Question

The mass of the earth is 6x10^24 kg and that of the moon is 7.4x10^22 kg. If the radius of the moon is 1740 km, then find the value of g if the earth is compressed into the size of moon.​

Answer 1

In the surface of the moon, gravitational acceleration is 1.63 m/s*2.

Step-by-step explanation:

An object of mass M will accelerate gravitationally at a distance R if it is at the following distance:

g = G*M/R^2

Where the gravitational constant is G.

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

At the surface of a moon, the distance between its surface and its center will be equal to its radius, since a moon's mass is concentrated at its center, thus:

R = 1740 km

It's important to remember that we need meters in order to work:

1 km = 1000 m

so:

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

R = 1740000 m

Basically, the mass consists of:

M = 7.4x10^22 kg

Incorporating all that into the gravitational acceleration equation, we get:

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

g = 1.63 m / s^2

In the surface of the moon, gravitational acceleration is 1.63 m / s*2.