5. The gravitational force between the two parts is

F =

Gm(M

− m)

r

2

=

G

r

2

mM

− m

2



which we differentiate with respect to m and set equal to zero:

dF

dm

= 0 =

G

r

2

(M

− 2m) =⇒ M = 2m

which leads to the result m/M = 1/2.

Document Outline

• Main Menu
• Chapter 1 Measurement
• Chapter 2 Motion Along a Straight Line
• Chapter 3 Vectors
• Chapter 4 Motion in Two and Three Dimensions
• Chapter 5 Force and Motion I
• Chapter 6 Force and Motion II
• Chapter 7 Kinetic Energy and Work
• Chapter 8 Potential Energy and Conservation of Energy
• Chapter 9 Systems of Particles
• Chapter 10 Collisions
• Chapter 11 Rotation
• Chapter 12 Rolling, Torque, and Angular Momentum
• Chapter 13 Equilibrium and Elasticity
• Chapter 14 Gravitation
  • 14.1 - 14.10
    • 14.1
    • 14.2
    • 14.3
    • 14.4
    • 14.5
    • 14.6
    • 14.7
    • 14.8
    • 14.9
    • 14.10
  • 14.11 - 14.20
    • 14.11
    • 14.12
    • 14.13
    • 14.14
    • 14.15
    • 14.16
    • 14.17
    • 14.18
    • 14.19
    • 14.20
  • 14.21 - 14.30
    • 14.21
    • 14.22
    • 14.23
    • 14.24
    • 14.25
    • 14.26
    • 14.27
    • 14.28
    • 14.29
    • 14.30
  • 14.31 - 14.40
    • 14.31
    • 14.32
    • 14.33
    • 14.34
    • 14.35
    • 14.36
    • 14.37
    • 14.38
    • 14.39
    • 14.40
  • 14.41 - 14.50
    • 14.41
    • 14.42
    • 14.43
    • 14.44
    • 14.45
    • 14.46
    • 14.47
    • 14.48
    • 14.49
    • 14.50
  • 14.51 - 14.60
    • 14.51
    • 14.52
    • 14.53
    • 14.54
    • 14.55
    • 14.56
    • 14.57
    • 14.58
    • 14.59
    • 14.60
  • 14.61 - 14.70
    • 14.61
    • 14.62
    • 14.63
    • 14.64
    • 14.65
    • 14.66
    • 14.67
    • 14.68
    • 14.69
    • 14.70
  • 14.71 - 14.80
    • 14.71
    • 14.72
    • 14.73
    • 14.74
    • 14.75
    • 14.76
    • 14.77
    • 14.78
    • 14.79
    • 14.80
  • 14.81 - 14.90
    • 14.81
    • 14.82
    • 14.83
    • 14.84
    • 14.85
    • 14.86
    • 14.87
    • 14.88
    • 14.89
    • 14.90
  • 14.91 - 14.94
    • 14.91
    • 14.92
    • 14.93
    • 14.94
• Chapter 15 Fluids
• Chapter 16 Oscillations
• Chapter 17 Waves—I
• Chapter 18 Waves—II
• Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
• Chapter 20 The Kinetic Theory of Gases
• Chapter 21 Entropy and the Second Law of Thermodynamics
• Chapter 22 Electric Charge
• Chapter 23 Electric Fields
• Chapter 24 Gauss’ Law
• Chapter 25 Electric Potential
• Chapter 26 Capacitance
• Chapter 27 Current and Resistance
• Chapter 28 Circuits
• Chapter 29 Magnetic Fields
• Chapter 30 Magnetic Fields Due to Currents
• Chapter 31 Induction and Inductance
• Chapter 32 Magnetism of Matter: Maxwell’s Equation
• Chapter 33 Electromagnetic Oscillations and Alternating Current
• Chapter 34 Electromagnetic Waves
• Chapter 35 Images
• Chapter 36 Interference
• Chapter 37 Diffraction
• Chapter 38 Special Theory of Relativity
• Chapter 39 Photons and Matter Waves
• Chapter 40 More About Matter Waves
• Chapter 41 All About Atoms
• Chapter 42 Conduction of Electricity in Solids
• Chapter 43 Nuclear Physics
• Chapter 44 Energy from the Nucleus
• Chapter 45 Quarks, Leptons, and the Big Bang