A simple pendulum is suspended from the ceiling of a car executing...

Given speed of the car, $v = 36 \text{ km/h} = 36 \times \dfrac{5}{18} \text{ m/s} = 10 \text{ m/s}$

Radius of the turn, $r = 10 \text{ m}$

Centripetal acceleration of the car is $a_c = \dfrac{v^2}{r} = \dfrac{10^2}{10} = 10 \text{ m/s}^2$

In the frame of the car, the pendulum bob experiences a pseudo force horizontally outward and the gravitational force downwards.

Balancing the forces in the frame of the car, with $T$ as the tension in the string and $\theta$ as the angle it makes with the vertical:

$T \sin\theta = m a_c$

$T \cos\theta = mg$

Dividing the two equations:

$\tan\theta = \dfrac{a_c}{g}$

Substituting the values of $a_c$ and $g$:

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

$\theta = 45^{{}^{{}^{\circ}}}$