Discuss the motion of particles in a central inverse-square-lawforce field for a superimposed force whose magnitude is inversely proportional to the cube of the distance from theparticle to theforce center.
Please see the attached file for the full question.

A particle of mass 50g moves under an attractive centralforce of magnitude 4r^3 dynes. The angular momentum is equal to l,000 g*cm/s.
a) Find the effective potential energy.
b) Indicate on a sketch of the effective potential the total energy for circular motion.
c) The radius of theparticle's orbit varies between ro an

A particle of unit mass is projected with speed (see attached) at right angles to the radius vector at a distance a from a fixed point O and is subjected to a force F(r) = μ/r^2, with μ a positive constant. Showthattheparticle moves on a path which passes the centre at a distance of 3a at its maximum.
See attached

A positively charged particle of mass 7.28E-8 kg is traveling due east with a speed of 85.7 m/s and enters a 0.290 T uniform magnetic field. Theparticle moves through one-quarter of a circle in a time of 2.08E-3 s, at which time it leaves the field heading due south. All during the motion theparticle moves perpendicular to the

A particle with a charge of 15.3 μC experiences a force of 2.43E-4 N when it moves at right angles to a magnetic field with a speed of 22.2 m/s. What force does this particle experience when it moves with a speed of 6.04 m/s at an angle of 23.5 ° relative to the magnetic field?
Please explain and solve problem.

A force of 5 Newtons acts in the direction of a = -7i+3j+4k, moving a particle from point B(1, 7, 1) to point C(-7, 5,-2). What is the work done on theparticle given thatthe displacement is measured in meters?

Which of the following statements are true about magnetic forces acting on charged or uncharged particles? Choose True or false for the following statements.
True False the magnetic force always acts parallel to the direction of motion of themoving charged particle.
True False the maximum magnetic forcethat a charged

I cannot figure out what equations to use or how to set up the following problem. It just seems like there is some data missing that i need. Any insight as to where to start would really help!
A radioactive source emits alpha-particles with kinetic energies of 4MeV. What must be the value of an applied magnetic field so th

A particle of mass 50g moves under an attractive centralforce of magnitude 4r^3 dynes. The angular momentum is equal to l,000 g*cm/s.
a) Find the effective potential energy.
b) Indicate on a sketch of the effective potential the total energy for circular motion.
c) The radius of theparticle's orbit varies between ro an