AIIMS 2018 Physics Dimensional Formula MCQ Question

The expression derived from the dimensional analysis shows that $v^2 \propto \lambda g$, indicating that velocity squared is directly proportional to the product of wavelength $\lambda$ and gravitational acceleration $g$. Option B, $v^2 \propto \lambda^2 g$, is incorrect because it suggests an additional power of $\lambda$ that does not align with the derived relationship. Other options also misrepresent the proportionality by either altering the powers of $g$ or $\lambda$ incorrectly, failing to satisfy the dimensional consistency established in the analysis. Thus, the correct relationship emphasizes the direct proportionality between $v^2$, $\lambda$, and $g$ as $v^2 \propto \lambda g$.