Physics - Circular Motion Question with Solution | TestHub

Let the frame of reference to be attached to the car with x-axis along horizontal direction and y-axis along vertical direction. Since the frame of reference is a rotating frame, a centrifugal force term should be added while applying Newton's second law.

Let $\theta$ be the angle made by the pendulum with the vertical.

Applying Newton's second law for horizontal direction:

$T\sin \theta -\frac{m{v}^2}{R}=0$  (since the acceleration of the pendulum in the rotating frame is 0).

$\therefore T\sin \theta =\frac{m{v}^2}{R}$    ..........(1)

Applying Newton's second law for vertical direction:

$T\cos \theta -mg=0$

$\Rightarrow T\cos \theta =mg$   ..........(2)

Dividing equation 1 by equation 2:

$$\begin{gathered} \tan \theta =\frac{v^2}{Rg}=\frac{{\left(20\right)}^2}{\left({\displaystyle 40}\right)\left(10\right)}=1 \\ \Rightarrow \theta =\frac{\pi }{4} \end{gathered}$$