I have a question about 21. the answer is a) 4.27 x 10^-8 N toward the 750 kg sp

Question

I have a question about 21.

the answer is
a) 4.27 x 10^-8 N toward the 750 kg sphere

b) 2.97m from the 750 kg sphere

I don't know how to solve each problems. please help me.

LI UCLA UN a. C Would you expect the period of an object orbiting the blatt greater hole with a semimajor axis of 1 AU to have a period . than, less than, or equal to 1 yr? Explain your reasoning b. N Use Equation 7.6 to calculate this period. (21. N Two spheres of mass M = 750 kg and M. = 350 kg are placed 5.00 m apart. A particle of mass m = 10.0 kg is now placed midway between the two spheres. . What is the net gravitational force on the particle due to the two spheres? b. At what position between the two spheres should the particle be placed so that the net gravitational force on the particle is zero? 22. E Estimate the magnitude of the gravitational force between the electron and proton in a hydrogen atom. 23. N The Lunar Reconnaissance Orbiter (LRO), with mass m 1850 kg, maps the surface of from altitude the Moon an Arhital ine a black hole whose mass IS LUI llllU

Explanation / Answer

a) Net force at midpoint = F = Gm/r^2(M1 - M2)

F = (6.67*10^-11*10/2.5^2)(750 - 350) = 4.27 x 10^-8 N (towards 750 kg)

b) Now GmM1/r^2 = GmM2/(5-r)^2

M1/r^2 = M2/(5-r)^2

750/r^2 = 350/(5-r)^2

(5 - r)/r = 0.68 ======> r = 2.98 from 750 kg sphere

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