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 the string of the pendulum with the vertical if this 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.

f = 10 m,

v = 36 km/hr

= 10 m/sec,

$g=10m/se{c}^2$

From the figure,

$Tsin\theta =\frac{m{v}^2}{r}...\left(i\right)$

$Tcos\theta =mg...\left(ii\right)$

$\Rightarrow \left(\frac{sin\theta }{cos\theta }\right)=\left(\frac{m{v}^2}{rmg}\right)$

$\Rightarrow tan\theta =\left(\frac{v^2}{rg}\right)$

$\Rightarrow \theta =ta{n}^{-1}\left(\frac{v^2}{rg}\right)$

$=ta{n}^{-1}\left[\frac{100}{(10\times 10)}\right]$

$=ta{n}^{-1}\left(1\right)$

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