In this question, we are given two statements and we need to determine which statements are correct.

Statement I: "The tropical year is shorter than the sidereal year." The tropical year refers to the time it takes for the Earth to complete one orbit around the Sun, while the sidereal year refers to the time it takes for the Earth to complete one orbit around the Sun relative to the fixed stars. The tropical year is actually longer than the sidereal year because of the precession of the Earth`s axis. So, Statement I is incorrect.

Statement II: "The solar day is longer than the sidereal day." The solar day refers to the time it takes for the Sun to return to its highest point in the sky, while the sidereal day refers to the time it takes for a fixed star to return to its highest point in the sky. Because of the Earth`s rotation on its axis, the solar day is slightly longer than the sidereal day. So, Statement II is correct.

Therefore, the correct answer is Option 2: "II only."