To solve this problem we will apply the concept given by the law of gravitational attraction, which properly defines gravity under the function
[tex]g = \frac{GM}{r^2}[/tex]
Here,
G = Gravitational Universal Constant
M = Mass of Earth
r = Distance between the human and the center of mass of the Earth
The acceleration due to gravity when is 4 times the mass of Earth and 3 times the radius would be given as,
[tex]g_1 = \frac{GM}{r^2}[/tex]
[tex]g_2 = \frac{G(4M)}{(3r)^2}[/tex]
[tex]g_2 = \frac{4GM}{9r^2}[/tex]
[tex]g_2 = \frac{4}{9} g_1[/tex]
The weight is defined as
[tex]W = mg_1[/tex]
So the new weight would be given as
[tex]W' = mg_2[/tex]
[tex]W' = m(\frac{4}{9} g_1 )[/tex]
[tex]W' = \frac{4}{9} mg_1[/tex]
[tex]W' = \frac{4}{9} W[/tex]
[tex]W' = \frac{4}{9}(650)[/tex]
[tex]W' = 288.8N[/tex]
Therefore the weight under this condition is 288.8N
