Rotational Motion Question 3

Question 3 - 25 January - Shift 1

A car is moving with a constant speed of 20 $m / s$ in a circular horizontal track of radius 40 $m$. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take $g=10$ $m / s^{2}$ )

(1) $\frac{\pi}{6}$

(2) $\frac{\pi}{2}$

(3) $\frac{\pi}{4}$

(4) $\frac{\pi}{3}$

Show Answer

Answer: (3)

Solution:

Formula: Banking Of Road Without Friction

$T \cos \theta=mg$

$T \sin \theta=\frac{mv^{2}}{R}$

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

$\tan \theta=\frac{20^{2}}{40 \times 10}$

$\tan \theta=1$

$\Rightarrow \theta=\frac{\pi}{4}$