A body has a weight of $w$ in the surface of the Earth. If the object is transported to a planet whose mass and radius is two times that of the Earth. Find its weight.

$\begin{array}{ll}

1.&4w\\

2.&2w\\

3.&\frac{w}{2}\\

4.&\frac{w}{4}\\

5.&w\\

\end{array}$

How should I calculate the weight of this object?.

On earth the only force acting in the object is given by the weight:

$F=mg=w$

And the gravitational force between two masses is given by:

$F=G\frac{m_1m_2}{r^2}$

Since it mentions that this object is moved to a planet which it has a radius which is two times that of the Earth and a mass double that of Earth then this becomes as:

$F_{2}=G\frac{m_1\cdot 2 m_2}{(2r)^2}=\frac{1}{2}G\frac{m_1m_2}{r^2}$

Therefore:

$w_{Planet}=\frac{1}{2}w_{Earth}$

But this doesn't make sense. What could I be doing wrong?. Shouldn't be the opposite. I mean two times that of the weight from Earth?. Can someone help me here?.