The correct answer is option 1: "Polar diameter is slightly less than the equatorial diameter". This means that the distance from one pole to the other pole of the Earth is slightly shorter than the distance measured around the Earth at the equator.

Option 2, which states that the polar and equatorial diameters are equal, is incorrect. The Earth is not a perfect sphere; it is slightly flattened at the poles and bulged at the equator due to its rotation. As a result, the polar diameter is shorter than the equatorial diameter.

Option 3, which claims that the polar diameter is longer than the equatorial diameter, is also incorrect. Again, due to the Earth`s bulging at the equator, the polar diameter is shorter.

Option 4 is also incorrect. The polar diameter is not half of the equatorial diameter.

In conclusion, option 1 accurately represents the relationship between the polar and equatorial diameters of the Earth. The slight flattening at the poles results in the polar diameter being slightly less than the equatorial diameter.