Question

A car is moving in a circular horizontal track of radius $10\text{m}$ with a constant speed of $10\text{m/s}$. A bob is suspended from the roof of the car by a light wire of length $1\text{m}$. The angle made by the wire with the vertical is
[Take $g=10{\text{m/s}}^2$]

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{6}$

Answer 1

The correct option is B $\frac{\pi }{4}$

Let the angle made by the wire with the verticle be $\theta$
Now, let us depict the situation as shown in the figure below


So, from the force equation which is applying on the bob we have
$T\sin \theta =\frac{m{v}^2}{r}\left(i\right)$
$T\cos \theta =mg\left(ii\right)$
From $\left(i\right)/\left(ii\right)$, we have
$\tan \theta =\frac{v^2}{rg}=\frac{{10}^2}{10\times 10}=1$
$\Rightarrow \theta =\frac{\pi }{4}$