Consider a particle of mass m executing motion in three dimensions under a central force potential...

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Consider a particle of mass m executing motion in three dimensions under a central force potential given by V(r) = Br, where a and B are constants and r denotes the radial distance from the origin of the coordinate system. The angular momentum of the particle is J and the total energy is E. (a) Calculate the minimum permissible value of energy E for a given J. (b) Derive the expression for the radius of a stable circular orbit. (c) Calculate the frequency of small radial oscillations about the stable circular orbit. (d) For a = 2 and B > 0, calculate the turning points of the orbit for a given energy E. Consider a particle of mass m executing motion in three dimensions under a central force potential given by V(r) = Br, where a and B are constants and r denotes the radial distance from the origin of the coordinate system. The angular momentum of the particle is J and the total energy is E. (a) Calculate the minimum permissible value of energy E for a given J. (b) Derive the expression for the radius of a stable circular orbit. (c) Calculate the frequency of small radial oscillations about the stable circular orbit. (d) For a = 2 and B > 0, calculate the turning points of the orbit for a given energy E.

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a To calculate the minimum permissible value of energy E for a given angular momentum J we need to find the point where the potential energy is at its minimum At this point the kinetic energy will be ... View the full answer