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)=2kr2, 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=nℏ, where
ℏ=h/(2pi),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?