Question

Given below are two statements:
Statement (I): If F is an irrotational vector field, then the angular velocity of the vector field is always greater than zero.
Statement (II): For a solenoidal vector function, the divergence is always zero.
Choose the most appropriate answer from the options given below:

• A. Both Statement I and Statement II are correct
• B. Both Statement I and Statement II are incorrect
• C. Statement I is correct but Statement II is incorrect
• D. Statement I is incorrect but Statement II is correct

Hint:

In vector calculus, irrotational fields have zero curl, and solenoidal fields have zero divergence.

Answer 1

The Correct Option is D

Statement (I) is incorrect because irrotational fields have zero curl, which does not imply the angular velocity is always greater than zero.
Statement (II) is correct because for a solenoidal vector field (a field with no divergence), the divergence is always zero.