1. For a simple pendulum undergoing small oscillations, the restoring torque gives angular acceleration

$\alpha = \frac{d^2\theta}{dt^2} = -\frac{g}{l}\,\theta$

where:

• $g$ is acceleration due to gravity,
• $l$ is length of pendulum,
• $\theta$ is angular displacement.

2. For the two pendulums:

$\alpha_1 = -\frac{g}{l_1}\theta_1$ $\alpha_2 = -\frac{g}{l_2}\theta_2$

3. Given that the angular accelerations are the same:

$\alpha_1 = \alpha_2$

So,

$-\frac{g}{l_1}\theta_1 = -\frac{g}{l_2}\theta_2$

4. Cancel $-g$ from both sides:

$\frac{\theta_1}{l_1} = \frac{\theta_2}{l_2}$

5. Cross-multiplying,

$\theta_1 l_2 = \theta_2 l_1$

6. Therefore, the correct option is:

$\boxed{\theta_1 l_2 = \theta_2 l_1}$

So, Option A is correct.