Question

A simple pendulum is suspended from the ceiling of a car taking a turn of radius 10 m at a speed of 36 km/h. Find the angle made by he string of the pendulum with the vertical if this angle does not change during the turn.

Answer 1

Speed of the car = v = 36 km/hr = 10 m/s
Acceleration due to gravity = g = 10 m/s²



Let T be the tension in the string when the pendulum makes an angle θ with the vertical.
From the figure, we get:
$$\begin{gathered} T\sin \theta =\frac{m{v}^2}{r}...\left(\mathrm{i}\right) \\ T\cos \theta =mg...\left(\mathrm{ii}\right) \\ \Rightarrow \frac{\sin \theta }{\cos \theta }=\frac{m{v}^2}{rmg} \\ \Rightarrow \tan \theta =\frac{v^2}{rg} \\ \Rightarrow \theta ={\tan }^{-1}\left(\frac{v^2}{rg}\right) \\ ={\tan }^{-1}\left[\frac{100}{(10\times 10)}\right] \\ ={\tan }^{-1}\left(1\right) \\ \Rightarrow \theta =45° \end{gathered}$$