Given below are two statements $ : $
Statement $I :$ When a system containing ice in equilibrium with water $(\text{liquid})$ is heated, heat is absorbed by the system and there is no change in the temperature of the system until whole ice gets melted.
Statement $II :$ At the melting point of ice, there is absorption of heat in order to overcome intermolecular forces of attraction within the molecules of water in ice, and the kinetic energy of molecules is not increased at the melting point.
In the light of the above statements, choose the correct answer from the options given below $ : $

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