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A circular track of radius 600 m is to b...

A circular track of radius 600 m is to be designed for cars at an average speed of 180 km/h. What should be the angle of banking of the track?

A

`tan^-1 (5/12)`

B

`tan^-1 (2/5)`

C

`tan^-1 (1/2)`

D

`tan^-1 (5/2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the angle of banking be `theta`. The forces on the car are ure.
a. weight of the car Mg downward and
b. normal force N.

For proper bnking sttic frictioN/Al force is not needed.
For vertical direction the acceleration is zero. So,
`N costheta=Mg` ..........i
for horizontal direection the acceleration is `v^2/r` towards the centre, so that
`N sintheta=Mv^2/r`..........ii
From i and ii
`tantheta=v^2/rg`
Putting the values `tantheta=((180 km/hr)^2)/((600 m)(10 m/s^2))=0.4167`
or, `theta=22.6^0`
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