A particle of mass m moves in a circular orbit in a central potential field `U(r)=U_o r^3`. where `U_o` is a constant. If Bohr's quantization condition is applied, radii of possible orbitals and energy levels vary with quantum number n as:

A body of mass m is situated in potential field U(x)=U_(o)(1-cospropx) where, U_(o) and prop are constants. Find the time period of small oscillations.

A particle of mass m moves in a one dimensional potential energy U(x)=-ax^2+bx^4 , where a and b are positive constant. The angular frequency of small oscillation about the minima of the potential energy is equal to

A particle of mass 2 kg moves in simple harmonic motion and its potential energy U varies with position x as shown. The period of oscillation of the particle is

A particle of mass 2 kg moves in simple harmonic motion and its potential energy U varies with position x as shown. The period of oscillation of the particle is

A particle of mass m in a unidirectional potential field have potential energy U(x)=alpha+2betax^(2) , where alpha and beta are positive constants. Find its time period of oscillations.

A particle of mass m moving along x-axis has a potential energy U(x)=a+bx^2 where a and b are positive constant. It will execute simple harmonic motion with a frequency determined by the value of

A particle of mass m moving along x-axis has a potential energy U(x)=a+bx^2 where a and b are positive constant. It will execute simple harmonic motion with a frequency determined by the value of

A small particle of mass m , moves in such a way that the potential energy U = ar^(3) , where a is position constant and r is the distance of the particle from the origin. Assuming Rutherford's model of circular orbits, then relation between K.E and P.E of the particle is :

A particle is moving in a circular path of radius a under the action of an attractive potential U=-(k)/(2r^(2)) . Its total energy is :

A test particle is moving in a circular orbit in the gravitational field produced by a mass density rho(r)=K/(r^(2)) . Indentify the correct relation between the radius R of the particle's orbit and its period T :