First slide

Banking of road

Question

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45⁰, the speed of the car is [CBSE AIPMT 2012]

Difficult

A

20 $m s^{- 1}$
B

30 $m s^{- 1}$
C

5 $m s^{- 1}$
D

10 $m s^{- 1}$

Solution

The angle of banking $\tan θ = \frac{v^{2}}{r g}$
Given, $θ = 45 °, r = 90 m and g = 10 {ms}^{- 2}$
$\tan 45 ° = \frac{v^{2}}{90 \times 10}$
$\Rightarrow v = \sqrt{90 \times 10 \times \tan 45 °}$
Speed of car, $v = 30 {ms}^{- 1}$

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