Laws of Motion - Result Question 58
58. A car is moving in a circular horizontal track of radius $10 m$ with a constant speed of $10 m /$ s. A bob is suspended from the roof of the car by a light wire of length $1.0 m$. The angle made by the wire with the vertical is
[NEET Kar: 2013]
(a) $0^{\circ}$
(b) $\frac{\pi}{3}$
(c) $\frac{\pi}{6}$
(d) $\frac{\pi}{4}$
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Answer:
Correct Answer: 58. (d)
Solution:
- (d) Given; speed $=10 m / s$; radius $r=10 m$ Angle made by the wire with the vertical is $\theta$. Then, $T \cos \theta=mg$
$ T \sin \theta=\frac{m v^{2}}{r} $
So,
$ \begin{aligned} & \tan \theta=\frac{v^{2}}{r g}=\frac{10^{2}}{10 \times 10}=1 \\ & \Rightarrow \theta=45^{\circ}=\frac{\pi}{4} \end{aligned} $
