The gravitational potential in a region is given by `V=20Nkg^-1(x+y)`. A. Show that the equation is dimensionally correct B. Find the gravitational field at the point `(x,y)` Leave your answer in terms of the unit vector `veci,vecj,veck`. C. Calculate the magnitude of the gravitational force on a particle of mass 500 g placed at the origin.

The gravitational potential in a region is given by `V=20Nkg^-1(x+y)`.

1.	The gravitational potential in a region is given by `V=20Nkg^-1(x+y)`. A. Show that the equation is dimensionally correct B. Find the gravitational field at the point `(x,y)` Leave your answer in terms of the unit vector `veci,vecj,veck`. C. Calculate the magnitude of the gravitational force on a particle of mass 500 g placed at the origin.
Answer» (a) `V=20(x+y)` `E_(x)=(delV)/(delx)=-20` `E_(y)=-(delV)/(dely)=-20` `vecE=E_(x)hati+E_(y)hatj` `=-20hati-20hatj` (b) `\|vecE\|=E=20sqrt(2)N//kg` `F=mE=0.5xx20sqrt(2)=10sqrt(2)N`

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