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 45^o, the speed of the car is

Moderate

A

5 m/s
B

10 m/s
C

20 m/s
D

30 m/s

Solution

According to question, angle of banking, $θ = 45^{0}$ .
Radius of curved road, r = 90 m and $g = 9.8 {ms}^{- 2} .$
Let the speed of car on the curved portion of road be $ν$ .
For no slip condition
$tanθ = (\frac{v^{2}}{rg})$
$\Rightarrow v = \sqrt{rg tanθ}$
$\Rightarrow v = \sqrt{90 \times 10 \times \tan (45^{\circ})}$
$= \sqrt{900} = 30 {ms}^{- 1}$

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