Question

A bus is moving in a circular horizontal track of radius $10m$ with a constant speed $10m/s$. A plumb bob is suspended from the roof of the bus by a light rigid rod of length $1.0m$. The angle made by the rod with the track is (Take $g=10m/s^2$):

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

Answer 1

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

From the figure,

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

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

From (i) and (ii) ,we get

$\tan \theta =\frac{\left(\frac{m{v}^2}{r}\right)}{mg}$

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

$\tan \theta =\frac{{10}^2}{10\times 10}$

$\tan \theta =1$

$\theta =45°$