Answer:
The weight of the body on the other planet would be 200 N
Explanation:
Recall that the acceleration of gravity at sea level on Earth is obtained via the general Gravitational force formula when the distance "d" is the radius of the Earth (R):
[tex]F=m\,g=G\,\frac{m\,\,m_E}{R^2} = m \,(G\,\frac{m_E}{R^2} )[/tex]
We are told that the weight of the object on Earth is 450 N, that is:
[tex]W=m\,g= m \,(G\,\frac{m_E}{R^2} )= 450[/tex]
in this other planet the acceleration of gravity will be different as shown below:
[tex](G\,\frac{m_E\,(1/9)}{(R/2))^2} )=(G\,\frac{m_E\,\,4}{R^2\,\,9} )=\frac{4}{9} (G\,\frac{m_E}{R^2} )[/tex]
so, its gravity is 4/9 that of the Earth, which now we can use to convert its weight (w) on the planet as 4/9 the weight it has on Earth:
[tex]w=m\,g_p=m\,\frac{4}{9} \,g=\frac{4}{9} \,450= 200\,\, N[/tex]
