Circular MotionMedium
Question
A car moving with a speed of $54\text{ }km/h$ takes a turn of radius 20 m . A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take $g = 10\text{ }m/s^{2}$ )
Options
A.$\tan^{- 1}(0.5)$
B.$\tan^{- 1}(0.75)$
C.$\tan^{- 1}(1.125)$
D.$\tan^{- 1}(0.25)$
Solution
Sol. [Key Concept: For a conical pendulum in the turning car $tan\theta = \frac{v^{2}}{rg}$ with $v = 15$ m/s, giving $tan\theta = \frac{225}{200} = 1.125$.]
$${tan\theta = \frac{v^{2}}{rg} }{\left( v = 54 \times \frac{5}{18} = 15\text{ }m/s \right) }{tan\theta = \frac{225}{20 \times 10} }{tan\theta = \frac{9}{8} }{\theta = \tan^{- 1}(1.125) }$$
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