A particle of mass \( m \) is moving in a circular orbit under the influence of the central force \( F(r)=-kr \), corresponding to the potential energy \( V(r)=\dfrac{kr^{2}}{2} \), where \( k \) is a positive force constant and \( r \) is the radial distance from the origin. According to the Bohr’s quantization rule, the angular momentum of the particle is given by \( L=n\hbar \), where \( \hbar=\dfrac{h}{2\pi} \), \( h \) is the Planck’s constant, and \( n \) a positive integer. If \( v \) and \( E \) are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?
