A

Step 1: Identify the parameters.
The given parameters are:
- Time period (T) = 2 s
- Distance (L) = 2.0 m
- Acceleration due to gravity (g) = 10 m/s²
Step 2: Calculate the angular velocity.
The angular velocity (ω) is given by the formula:
$$ ext{ω} = \frac{2\pi}{T}$$
Substituting the values,
$$\text{ω} = \frac{2\pi}{2} = \pi ext{ rad/s}$$
Step 3: Determine the radius of the circular motion.
The height (h) of the pendulum can be calculated using:
$$h = L\sin(\theta)$$
The horizontal component (r) of the motion is:
$$r = L\cos(\theta)$$
Using the right triangle relationship and the time period relations, we know that:
$$g/L = \frac{\omega^2}{L} \implies \text{tan}(\theta) = \frac{L}{h}$$
Hence,
$$h = \frac{g}{\omega^2} = \frac{10}{\pi^2}$$
Given h = 2.0 m, we can calculate the retardation (a).
Step 4: Relate the forces.
The effective force experienced is the combination of g and a (the retardation of lift):
We set up the equation as follows:
$$g - a = \frac{L\omega^2}{L}$$
Substituting the values,
$$10 - a = 2\pi^2$$
Solving for a,
$$a = 10 - 2\pi^2$$
Substituting $$\pi^2 \approx 9.87$$, we get
$$a \approx 10 - 19.74 = -9.74 ext{ m/s}^2$$
Since it’s retardation, we take the positive value.
Step 5: Finalize the answer.
Therefore, the retardation of the lift is approximately $9.74 ext{ m/s}^2$.
Hence, the final answer is A.