Question

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

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

Answer 1

Answer: (C)

${45}^{\circ }$

Let the angle made by the rod with the track is $\theta$
Let the tension in the string be T

$T\cos \theta =\frac{m{v}^2}{r}$ ....(1)

$T\sin \theta =mg$.......(2)

Dividing (2) by (1)

$\frac{\sin \theta }{\cos \theta }=\frac{g}{\frac{v^2}{r}}=\frac{gr}{v^2}$

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

$\Rightarrow \theta ={45}^{\circ }$