First slide

Circular motion in horizontal plane

Question

A car is travelling at 36 kmph on a road. If µ = 0.5 between the tyres and the road, the minimum turning radius of the car is (g=10ms^–2)

Moderate

A

20m
B

25m
C

30m
D

35m

Solution

Speed of car = $\frac{36000}{3600} m / s = 10 m / s$

Frictional force acting on the car
$f=\frac {mV^2}{r}$

f_l = µN = µmg
For no skidding, f ≤ f_l

$\Rightarrow \frac {mV^2}{r}\leq \mu mg$

$\Rightarrow r\geq \frac {V^2}{\mu g}$

$\therefore r_{min}= \frac {V^2}{\mu g}=\frac {10X10}{0.5X10}m=20m$

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