The new weight is 273.8 N
Explanation:
The weight of an object on Earth is given by
[tex]W=mg[/tex]
where
m is the mass of the object
g is the acceleration of gravity
The acceleration of gravity at the Earth's surface can be rewritten as
[tex]g=\frac{GM}{R^2}[/tex]
where
G is the gravitational constant
M is the Earth's mass
R is the Earth's radius
Substituting into the previous equation,
[tex]W=\frac{GMm}{R^2}[/tex]
We said that in normal conditions, the weight of the person is 730 N:
[tex]W=\frac{GMm}{R^2}=730 N[/tex]
Later, we are said that:
Substituting into the equation, we find the new weight of the person in these conditions:
[tex]W'=\frac{G(6M)m}{(4R)^2}=\frac{6}{16}(\frac{GMm}{R^2})=\frac{3}{8}W[/tex]
So, the new weight is 3/8 of the original weight, therefore:
[tex]W'=\frac{3}{8}(730)=273.8 N[/tex]
Learn more about gravity:
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