A pendulum is hanging from the ceiling of a car having an acceleration `a_0` with respect to the road. Find the angle made by the string with the vertical.

Explanation

To find the angle made by the string of a pendulum with the vertical when the pendulum is hanging from the ceiling of a car that is accelerating with respect to the road, we can follow these steps:

### Step 1: Identify the Forces Acting on the Pendulum Bob
The forces acting on the pendulum bob of mass \( m \) are:
- The gravitational force \( \vec{F_g} = mg \) acting downward.
- The tension \( \vec{T} \) in the string acting along the string.
- A pseudo force \( \vec{F_p} = ma_0 \) acting horizontally in the opposite direction of the car's acceleration \( a_0 \).

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