Question

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 $m{s}^{-1}$. A plumb bob is suspended from the roof of the car by a light rigid rod. The angle made by the rod with the vertical is

• A. Zero
• B. ${30}^0$
• C. ${45}^0$
• D. ${60}^0$

Answer 1

The correct option is C ${45}^0$

Hence from the figure,

We know that,

$T\sin \theta =\frac{{mv}^2}{r}$ [centripetal] $⟶\left(i\right)$

$T\cos \theta =mg⟶\left(ii\right)$ (force)

from $\left(i\right)$ and $\left(ii\right))$

$\frac{T\sin \theta }{T\cos \theta }=\frac{{mv}^2}{r}\times \frac{1}{mg}$

$\tan \theta =\frac{v^2}{rg}$

Given that, radius $=10$ m

velocity $=10$ m/s

$g=10m/s^2$

$tan\theta =\frac{{10}^2}{10\times 10}=1\Rightarrow \theta ={45}^0$