Question

A car is moving on a circular horizontal track of radius $10m$ with a constant speed of $10m{s}^{-1}$. The angle made by the road with track is (Take $g=10m/s^2$)

• A. $\text{zero}$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${45}^{\circ }$


By the free body diagram and writing the force equation we get,

$N\cos \theta =mg...\left(i\right)$
$N\sin \theta =\frac{m{v}^2}{r}...\left(ii\right)$
Now by dividing both the above equations, we get,
$\theta ={\tan }^{-1}\left(\frac{v^2}{rg}\right)$
where, $v$ = speed and r = radius
$\therefore \tan \theta =\frac{(10{)}^2}{10\times g}=1$
$\Rightarrow \theta ={45}^{\circ }$