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Saturday, April 21

Detailed notes on "A body moving under central force"

21 April Physics , 0 Comments

Detailed Topics

  • Central Force
  • Properties of central force
  • Equation of body moving under central force
  • Prove that A body moving under central force have

  1.         Angular momentum of a body will always remains conserve i.e.            J = constant
  2.        Areal velocity is constant.
  3.        The planet of orbit will always remains fixed.
  • Conservation of energy when a particle moves under a central force
  • Differential equation of a body moving under central force
  • Classification of orbit

  • Nature of orbit

Numerical problems

 Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius.

 Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius.

 Que 3) A particle is moving in a path given by r = a(1 + Cos θ)  show that the force acting on the particle is inversely proportional to fourth of its radius.

 Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by
e = (Umax - Umin)/(Umax + Umin)
Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)

Detailed Topics Central Force Properties of central force Equation of body moving under central force Prove that A body moving under central force have Angular momentum of a body will always remains conserve i.e. J = constant Areal velocity is constant. The planet of orbit will always remains fixed. Conservation of energy when a particle moves under a central force Differential equation of a body moving under central force Classification of orbit Nature of orbit Numerical problems Que 1) A particle is moving in a path given by r = 2a Cos θ show that the force acting on this particle is inversely proportional to fifth power of its radius. Que 2) A particle is moving in a path given by r = eθ show that the force acting on the particle is inversely proportional to cube of its radius. Que 3) A particle is moving in a path given by r = a(1 + Cos θ) show that the force acting on the particle is inversely proportional to fourth of its radius. Que 4) A planet revolve around the sun in an elliptical orbit having Umax and Umin are the velocities. Show that the eccentricity is given by e = (Umax - Umin)/(Umax + Umin)



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