Given below are two statements:
Statement $I$: For a mechanical system of many particles,the total kinetic energy is the sum of the kinetic energies of all the particles.
Statement $II$: The total kinetic energy can be expressed as the sum of the kinetic energy of the center of mass with respect to the origin and the kinetic energy of all the particles with respect to the center of mass as the reference frame.
In the light of the above statements,choose the correct answer from the options given below:

• A
  Both Statement $I$ and Statement $II$ are true
• B
  Statement $I$ is true but Statement $II$ is false
• C
  Statement $I$ is false but Statement $II$ is true
• D
  Both Statement $I$ and Statement $II$ are false