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  4. While driving a car around a curve of 200 m radius, the driver notices that a simple pendulum hung to the roof of the car is making an angle of 15° to the horizontal. The speed of the car in kmh-1 is

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Q. While driving a car around a curve of 200 m radius, the driver notices that a simple pendulum hung to the roof of the car is making an angle of 15$^\circ$ to the horizontal. The speed of the car in $kmh^{-1}$ is

KEAMKEAM 2003Motion in a Plane

Solution:

Angle $\theta$ is given by
$\tan \, \theta = \frac{v^2}{rg} $
or $\nu^2 = 529.2$ (with the substitution)
$\Rightarrow $ $\nu = 23\,ms^{-1}$
or $\nu = 23 \times \frac{18}{5} = 82.5\, kmh^{-1}$