Answer:
The weight of the body in the new planet is 100 newtons.
Explanation:
From Newton's Law of Gravitation we find that gravitational force is directly proportional to mass of the planet and inversely proportional to the square of its radius. From this fact we can build the following relationship:
[tex]\frac{F_{1}\cdot R_{1}^{2}}{M_{1}} = \frac{F_{2}\cdot R_{2}^{2}}{M_{2}}[/tex] (1)
Where:
[tex]F_{1}[/tex], [tex]F_{2}[/tex] - Gravitational force, measured in newtons.
[tex]M_{1}[/tex], [tex]M_{2}[/tex] - Mass of planet, measured in kilograms.
[tex]R_{1}[/tex], [tex]R_{2}[/tex] - Radius of the planet, measured in meters.
If we know that [tex]F_{1} = 800\,N[/tex], [tex]\frac{M_{2}}{M_{1}} = \frac{1}{2}[/tex] and [tex]\frac{R_{2}}{R_{1}} = 2[/tex], then the expected gravitational force in the new planet is:
[tex]F_{2} = F_{1}\cdot \left(\frac{M_{2}}{M_{1}} \right)\cdot \left(\frac{R_{1}} {R_{2}}\right)^{2}[/tex]
[tex]F_{2} = (800\,N)\cdot \left(\frac{1}{2} \right)\cdot \left(\frac{1}{2}\right)^{2}[/tex]
[tex]F_{2} = 100\,N[/tex]
The weight of the body in the new planet is 100 newtons.
