Question

A car is moving in a circular horizontal track of radius $10\text{m}$ with a constant speed of $10{\text{ms}}^{-1}$. A plumb bob is suspended from the roof of the car by a string of length $1\text{m}$. The angle made by the string with the track is $(g=10{\text{ms}}^{-2})$ :

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

Answer 1

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


From the figure, we know that,
$T\sin \theta =\frac{m{v}^2}{r}...\left(i\right)$
and
$T\cos \theta =mg....\left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$,

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

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

Given that, $r=10\text{m}$
$v=10\text{m/s}$
$g=10{\text{m/s}}^2$

$\therefore \tan \theta =\frac{{10}^2}{10\times 10}=1$
$\Rightarrow \theta ={45}^{\circ }$
Angle made with the track is $90-\theta ={90}^o-{45}^o={45}^o$