Question

Brendan drew a diagram to illustrate the centripetal force acting on a satellite.

An illustration of the earth with an illustration of a satellite on the circle. There are two vectors from the satellite, one tangent to the circle and clockwise labeled v and the other tangent to the circle and counterclockwise labeled F Subscript g Baseline = F Subscript c Baseline. There is a radius of the circle labeled r.
How can Brendan correct his diagram?

Draw the Fg = Fc vector so it points at a 45° angle from the v vector.
Change the Fg = Fc vector label so it reads Fa = Fc.
Draw the Fg = Fc vector so it is longer than the v vector.
Change the Fg = Fc vector so it is perpendicular to the v vector.

Answer 1

Correct answer: Change the Fg = Fc vector so it is perpendicular to the v vector.

Why: for uniform circular motion the velocity vector is tangent to the circle and the centripetal force (here gravity) is directed radially inward toward the centre. That makes the force vector perpendicular (90°) to the velocity.

Notes on the other choices: 45° is wrong (force must point to centre), the label Fg = Fc is fine (gravity provides the centripetal force), and comparing the drawn lengths of a force vector and a velocity vector is meaningless (they have different units), so you should not make the force simply "longer" than v.