Question

A road of average radius R = 50 m is banked for speed 36 km/h assuming no friction. But the track is rough and coefficient of friction between the tyre of vehicle and road is 0.3. Then which one of the following options is wrong? [g = 10 m/s2]

Answer 1

Answer:

I hope this is helpful to you

Answer 2

Given:

A road of average radius R = 50 m is banked for speed 36 km/h assuming no friction. But the track is rough and coefficient of friction between the tyre of vehicle and road is 0.3 , [g = 10 m/s2] .

To Find:

Speed of vehicle?

Solution:

It is given that -

Average radius of road ,R=50m,

speed of vehicle when there is no friction,$v_{1}=36km/h=10m/s$

therefore,

from the formula of speed when there is no friction is;

$(v_{1} )^{2}=gR (tan\theta)\\\\100=10\times50(tan\theta)\\\\tan\theta= 1/5\\\\\theta=tan^{-1}(1/5)$

now, assuming there is friction and coefficient of friction is given which is equal to μ = 0.3

therefore,

from the formula of safe speed;

$v_{2} = \sqrt{\mu Rg}$

⇒ $v_{2}=\sqrt{0.3\times10\times50} \\\\=10\sqrt{1.5}m/s$

Hence, speed of vehicle is $10\sqrt{1.5} m/s$ when coefficient of friction is given.