Conservation of Energy question from MHT CET 2024 (16 May, Shift 1)

Answer: (d)

1. Height at the extreme: $h = L(1 - \cos\theta) \approx \frac{L\theta^2}{2}$ for small $\theta$.
2. Amplitude $A = L\theta \Rightarrow \theta = \frac{A}{L}$, so $h = \frac{A^2}{2L}$.
3. $U = mgh = \frac{mgA^2}{2L}$
4. So the answer is (d) $\frac{mgA^2}{2L}$.