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 vertical is $(g=10{\text{ms}}^{-2})$

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

Answer 1

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

By the free body diagram of the mass
Hence 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, $r=10\text{m}$
$v=10\text{m/s}$
$g=10{\text{m/s}}^2$

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

Hence option C is the correct answer