For a curved track of radius R, banked at angle θ (Take v0 = $\sqrt{Rg\tan\theta}$ )

For No friction & safely turn$\frac{mv_{0}^{2}}{R}\cos\theta = mg\sin\theta$$\boxed{v_{0} = \sqrt{Rg\tan\theta}}$Vmin < V0 < VmaxIn Vmin & Vmax must be come into play for safely turn maximum value of angle of banking$\boxed{\theta = \tan^{- 1}\mu_{0}}$

Circular MotionHardBloom L3

Question

For a curved track of radius R, banked at angle θ (Take v₀ = $\sqrt{Rg\tan\theta}$ )

Options

A.a vehicle moving with a speed v₀ is able to negotiate the curve without calling friction into play at all

B.a vehicle moving with any speed V > V₀ is always able to negotiate the curve, with friction called into play

C.a vehicle moving with any speed V < V₀ must have the force of friction into play

D.the minimum value of the angle of banking for a vehicle parked on the banked road can stay there without slipping, is given by θ = tan^–1 µ₀ (µ₀ = coefficient of static friction)

Solution

For No friction & safely turn

$\frac{mv_{0}^{2}}{R}\cos\theta = mg\sin\theta$

$\boxed{v_{0} = \sqrt{Rg\tan\theta}}$

V_min < V₀ < V_max

In V_min & V_max must be come into play for safely turn maximum value of angle of banking

$\boxed{\theta = \tan^{- 1}\mu_{0}}$

Create a free account to view solution

View Solution Free

Topic: Circular Motion·Practice all Circular Motion questions

More Circular Motion Questions

A particle is in motion on the x-axis. The variation of its velocity with position is as shown. The graph is circle and ...A car is going on an overbridge of radius R, maintaining a constant speed. As the car is descending on the overbridge fr...The minimum frequency of photon required to break a particle of mass 15.348 amu into $4\alpha$ particles is $\_\_\_\_$ k...A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended ...Three identical particles are joined together by a thread as shown in figure. All the three particles are moving on a sm...