A particle of mass m approaches a region of force starting from `r=+infty` The potential energy function in terms of distance r from the origin is given by,
`U(r) = K/(2a^(3))(3a^(2)-r^(2)) for 0 lt r lt a`
`=K//r for r gt a`
(a) Derive the force F(r) and determine whether it is repulsive or attractive.
(b) With what velocity should the particle start at `r=infty` to cross over to other side of the origin.
(c) If the velocity of the particle at `r= infty` is `sqrt((2K)/(am))` towards the origin describe the motion.

The potential energy function of a particle is given by U(r)=A/(2r^(2))-B/(3r) , where A and B are constant and r is the radial distance from the centre of the force. Choose the correct option (s)

The potential energy function of a particle is given by U(r)=A/(2r^(2))-B/(3r) , where A and B are constant and r is the radial distance from the centre of the force. Choose the correct option (s)

A particle of mass m lies at a distance r from the centre of earth. The force of attraction between the particle and earth as a function of distance is F(r ),

The potential energy of a two particle system separated by a distance r is given by U(r ) =A/r where A is a constant. Find to the radial force F_(r) , that each particle exerts on the other.

The potential energy of a two particle system separated by a distance r is given by U(r ) =A/r where A is a constant. Find to the radial force F_(r) , that each particle exerts on the other.

IF a particle of mass m is moving in a horizontal circle of radius r with a centripetal force (-(K)/(r^(2))) , then its total energy is

If the gravitational force had varied as r^(-5//2) instead of r^(-2) the potential energy of a particle at a distance 'r' from the centre of the earth would be proportional to

In a conservative force field we can find the radial component of force from the potential energy function by using F = -(dU)/(dr) . Here, a positive force means repulsion and a negative force means attraction. From the given potential energy function U(r ) we can find the equilibrium position where force is zero. We can also find the ionisation energy which is the work done to move the particle from a certain position to infinity. Let us consider a case in which a particle is bound to a certain point at a distance r from the centre of the force. The potential energy of the particle is : U(r )=(A)/(r^(2))-(B)/(r ) where r is the distance from the centre of the force and A andB are positive constants. Answer the following questions. If the total energy of the particle is E=-(3B^(2))/(16A) , and it is known that the motion is radial only then the velocity is zero at

In a conservative force field we can find the radial component of force from the potential energy function by using F = -(dU)/(dr) . Here, a positive force means repulsion and a negative force means attraction. From the given potential energy function U(r ) we can find the equilibrium position where force is zero. We can also find the ionisation energy which is the work done to move the particle from a certain position to infinity. Let us consider a case in which a particle is bound to a certain point at a distance r from the centre of the force. The potential energy of the particle is : U(r )=(A)/(r^(2))-(B)/(r ) where r is the distance from the centre of the force and A andB are positive constants. Answer the following questions. If the total energy of the particle is E=-(3B^(2))/(16A) , and it is known that the motion is radial only then the velocity is zero at