A

Step 1: Understand the concept of surface tension. Surface tension is the property of a liquid's surface that allows it to resist an external force, due to the cohesive nature of its molecules. It is caused by the attraction between molecules at the surface of a liquid compared to those in the bulk of the liquid.

Step 2: Compare surface tensions. Water has a high surface tension (8 dyne/cm) compared to most oils, which means that the molecules at the surface of the water are more strongly attracted to each other than to the oil molecules. This results in oil being unable to penetrate or spread over the water surface effectively.

Step 3: Evaluate the options:

• Option A: Surface tension of water is very high - This is correct, as high surface tension prevents oil from spreading over it.
• Option B: Surface tension of water is very low - Incorrect, as water's surface tension is among the highest.
• Option C: Viscosity of oil is high - While oil often has a higher viscosity, it does not directly explain why water does not spread over it.
• Option D: Viscosity of water is high - This is not true, and it does not relate to the question.

Conclusion: The main reason oil spreads on water is due to the high surface tension of water, which creates a barrier against the oil exceeding these attractive forces. Therefore, the correct answer is A.