In a bizarre solar system, three equivalent stars, each of mass M, revolve in ci
ID: 2257313 • Letter: I
Question
In a bizarre solar system, three equivalent stars, each of mass M, revolve in circular orbits
of radius R about their center of mass which is at the center of the circle. The stars are
arranged at the corners of an equilateral triangle (which revolves with the stars). What is
the magnitude of the gravitational ?eld at the center of the circle? [Hint: Use superposition
and symmetry, and remember that the gravitational ?eld is a vector.]
(a) 3GM/R2
(b) GM/R2
(c) ?
3GM/R2
(d) 0
The answer is(d) ,Can you explain why
Explanation / Answer
each will exert gravitational force equal in magnitude but different in direction.
also for unit vectors, starting from center of an equilateral triangle to its vertices,
their vector sum is 0 (cancelling each other's components in x and y)
hence net force will be 0 (being a vector quantity)