Simple Pendulum question from JEE Main 2024 (5 Apr, Shift 1)

Answer: (a)

1. $g \propto \frac{1}{r^2}$ and $T \propto \frac{1}{\sqrt{g}} \Rightarrow T \propto r$ (distance from earth's centre).
2. At height $R$: $r_1 = 2R$; at height $2R$: $r_2 = 3R$.
3. $\frac{T_2}{T_1} = \frac{3}{2} \Rightarrow 2T_2 = 3T_1$.
4. So the answer is (a) $3T_1 = 2T_2$.