First slide

Circular motion in horizontal plane

Question

For a car taking a turn on a horizontal surface, let N₁ and N₂ be the normal reactions of the road on the inner and outer wheels respectively.

Moderate

A

N₁ is always greater than N₂
B

N₂ is always greater than N₁
C

N₁ is always equal to N₂
D

Either (a) or (b) depending on the speed of the car and the radius of curvature of the road.

Solution

N₁+N₂ = mg .....................(1)
Taking moment of all forces about the point of contact of outer wheels with the road surface ,
$N_1\;X\;b +\frac{mv^2}{r}\;X\;h=mg \;X\;b/2.............(2)$
Solving , $\large N_1=(\frac{mg}{2}-\frac{mv^2}{r}.\frac{h}{b})\;N_2=(\frac{mg}{2}+\frac{mv^2}{r}.\frac{h}{b})$

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