If the radius of gyration of a compound pendulum about an axis through e.g. is more, then its frequency of oscillation will be

The frequency of oscillation of a compound pendulum is inversely proportional to the radius of gyration about the axis of rotation. The radius of gyration (k) is a measure of how mass is distributed relative to the axis of rotation. A larger radius of gyration means the mass is more spread out, leading to a lower frequency of oscillation.

Let's analyze each option:

Option A: "Less" - This is correct because a larger radius of gyration results in a longer period of oscillation, thus reducing the frequency.

Option B: "More" - This is incorrect as frequency decreases with an increase in the radius of gyration.

Option C: "Same" - This is incorrect because frequency and radius of gyration are inversely related.

Option D: "Data are insufficient to determine same" - This is incorrect because the relationship between frequency and radius of gyration is well-established in physics.

Therefore, the correct answer is Option A: Less.