The angle of banking for a cyclist taking a turn at a curve is given by tan$\mathrm{\theta } = \frac{{\mathrm{v}}^{\mathrm{n}}}{\mathrm{rg}}$ where symbols have their usual meaning. The value of n is:

A car of mass \(1000\) kg negotiates a banked curve of radius \(90\) m on a frictionless road. If the banking angle is of \(45^\circ,\) the speed of the car is:

The banking angle for a curved road of radius \(490\) m for a vehicle moving at \(35\) m/s is:
1. ${\tan }^{-1}(0.25)$
2. ${\tan }^{-1}(0.55)$
3. ${\tan }^{-1}(0.45)$
4. ${\tan }^{-1}(0.75)$

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle formed by the rod with respect to the vertical is: