Question

Two identical starts, a fixed distance D apart, revolve in a circle about their mutual center of mass, as shown. Each star has a mass M and speed v. G is the universal gravitational constant. Which of the following is a correct relationship among these quantities?

Answer 1

The correct relationship among the given quantities (M, D, v, G) is v^2 = G*M/D. This is derived by equating the formulas for gravitational force and centripetal force.

Step-by-step explanation:

In this case, we are dealing with the concept of gravitational force and circular motion. The gravitational force between the two masses (stars) is given by the formula: F = G*M^2/D^2 where 'G' is the universal gravitational constant, 'M' is the mass of the stars, and 'D' is the distance between the two masses.

Also, this gravitational force provides the centripetal force for the circular motion of the stars, which is given by: F = M*v^2/r where 'v' is the speed of the stars and 'r' is the radius of the circular path (in this case, r = D/2).

Equating the two formulas, we can derive the correct relationship among these quantities: G*M^2/D^2 = M*v^2/(D/2). Simplifying this, we get v^2 = G*M/D as the correct relationship.