1. Identify the acceleration of the car

Since the car moves in a horizontal circle with constant speed, it has centripetal acceleration:

$a_c = \frac{v^2}{r}$

Given:

$v = 20\ \text{m/s}, \quad r = 40\ \text{m}$

So,

$a_c = \frac{20^2}{40} = \frac{400}{40} = 10\ \text{m/s}^2$

2. For the suspended bob inside the car

In the non-inertial frame of the car, the bob experiences:

• weight downward: $mg$
• pseudo force horizontally outward: $ma_c$
• tension along the string

The string aligns with the resultant of $mg$ and pseudo force.

If $\theta$ is the angle made by the string with the vertical, then

$\tan \theta = \frac{\text{horizontal acceleration}}{\text{vertical acceleration}} = \frac{a_c}{g}$

Substitute values:

$\tan \theta = \frac{10}{10} = 1$

Therefore,

$\theta = 45^\circ = \frac{\pi}{4}$

3. Check options

• A: $\frac{\pi}{2}$  incorrect
• B: $\frac{\pi}{6}$  incorrect
• C: $\frac{\pi}{4}$  correct
• D: $\frac{\pi}{3}$  incorrect

Hence, the correct option is C.