Three point particles are fixed in place in an xy plane. Particle A has mass mA = 5 g, particle B has mass 2.00 mA, and particle C has mass 3.00 mA. A fourth particle D, with mass 4.00 mA, is to be placed near the other three particles. What (a) x coordinate and (b) y coordinate should particle D be placed so that the net gravitational force on particle A from particles B, C, and D is zero. please write the step by step process on paper.

A planet of mass 5 ⨯ 1024 kg is at location <4 ⨯ 1011, −4 ⨯ 1011, 0> m.  A star of mass 4 ⨯ 1030 kg is at location <−6 ⨯ 1011, 4 ⨯ 1011, 0> m. (a) What is the relative position vector pointing from the planet to the star? (b) What is the distance between the planet and the star? (c) What is the unit vector in the direction of r? (d) What is the magnitude of the force exerted on the planet by the star?(e) What is the magnitude of the force exerted on the star by the planet? (f) What is the force (vector) exerted on the planet by the star? (g) What is the force (vector) exerted on the star by the planet? (Note the change in units.)

Three point particles are fixed in position in an xy plane. Two of them, particle A of mass 6 g and particle B of mass 11 g, are shown in the figure with a separation of dAB = 0.555 m at angle = 30°. Particle C, with mass 7 g, is not shown. The net gravitational force acting on particle A due to particles B and C is 2.31 x 10- N at an angle of -163.8°. from the positive x axis. What are (a) the x coordinate and (b) the y coordinate of particle C? 14 B (a) Number: dAB 0 i (b) Number: i A Units: Units: < <

The center of a moon of mass m is a distance D from the center of a planet of mass M. At some distance x from the center of the planet, along a line connecting the centers of planet and moon, the net force on an object will be zero. Derive an expression for x.