Question

A simple pendulum is suspended from the ceiling of a car taking a turn of radius $10m$ at a speed of $36km/h$. Find the angle (in degree) made by the string of the pendulum with the vertical if this is angle does not change during the turn. Take $g=10m/s^2$.

Answer 1

A pendulum is suspended from the ceiling of a car taking a turn
$r=10m,v=36km/hr=10m/sec,g=10m/{sec}^2$
from the figre $T\sin \theta =\frac{m{v}^2}{r}...\left(i\right)$
$T\cos \theta =mg...\left(ii\right)$
$\Rightarrow \frac{\sin \theta }{\cos \theta }=\frac{m{v}^2}{rmg}\Rightarrow \tan \theta =\frac{v^2}{rg}\Rightarrow \theta ={\tan }^{-1}\left(\frac{v^2}{rg}\right)={\tan }^{-1}\left(\frac{100}{10\times 10}\right)={\tan }^{-1}\left(1\right)\Rightarrow \theta ={45}^o$