Q153 / 180 · COMEDK 2013 · Physics

A car is moving in a circular horizontal track of radius $10 \mathrm{~m}$ with a constant speed of $10 \mathrm{~m} / \mathrm{s}$. A bob is suspended from the roof of the car by a light wire of length $1.0 \mathrm{~m}$. The angle made by the wire with the vertical is

  • A
    $\frac{\pi}{3}$
  • B
    $\frac{\pi}{6}$
  • Correct answer
    C
    $\frac{\pi}{4}$
  • D
    $0^{\circ}$

Solution

Given, $r=10 \mathrm{~m}, v=10 \mathrm{~m} / \mathrm{s}$ If $\theta$ be the angle made by the wire with the vertical, then $$ \begin{aligned} \tan \theta &=\frac{v^{2}}{r g} \\ &=\frac{(10)^{2}}{(10)(10)}=1 \\ \Rightarrow \quad \theta &=45^{\circ} \text { or } \frac{\pi}{4} \end{aligned} $$

Hence, the correct answer is option: 'C'.

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