Answer:
We know that the gravitational acceleration in the surface of the Earth can be written as:
g = G*M/r^2
Where:
M = mass of the Earth
r = radius of the Earth.
G = gravitational constant.
The weight of an object of mass m, is written as:
W = m*g = m*(G*M/r^2)
Now, if we move our object to a place that has a mass equal to 1/6 times the mass of the Earth, and 1/3 the radius of the earth.
The gravitational acceleration on this planet is written as:
g' = G*(M/6)/(r/3)^2 = (1/6)*(G*M)/(r^2/9) = (9/6)*(G*M/r^2) = (3/2)*g
then the weight on this planet is:
W' = m*g' = m*(3/2)*g = (3/2)*(m*g)
and m*g was the weight on Earth, then:
W' = (3/2)*(m*g) = (3/2)*W
The new weight is 3/2 times the weight on Earth.
