The value of the gravitational field in a region is given by g = 2i + 3j. What is the change in gravitational potential energy of a particle of mass 5kg when it is taken from the origin O(0,0) to a point P(10, -5)? (Letters in bold are vectorial representations)

25 J

The gravitational potential energy, in vectorial mathematics, is the dot product of the gravitational field and relative position multiplied by mass.

Gravitational potential energy = (g . P) x m

= [(2i + 3j) .(10i – 5j)] x 5

= (20 – 15) x 5

= 25 J.