A point mass is fixed at the origin in otherwise empty space

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A point mass

M

is fixed at the origin in otherwise empty space. (i) Explain why the gravitational potential

V

at a distance

r

from the mass is negative for all finite values of

r

when the zero of potential is taken at infinity. (ii) Show how the variation of

V

with

r

qualitatively indicates the relative strength of the gravitational field intensity

g

at different distances. (iii) On the same set of axes, sketch the expected shapes of the graphs of

V(r)

and

g(r)

for

r>0

. Clearly mark the region where the field is stronger and where it is weaker, and justify your markings.