Question

Statement I: A cyclist is moving on an unbanked road with a speed of 7 kmh^-1 and takes a sharp circular turn along a path of radius of 2 m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve. (g = 9.8 m/s²)

Statement II: If the road is banked at an angle of 45°, cyclist can cross the curve of 2 m radius with the speed of 18.5 kmh^-1 without slipping.

In the light of the above statements, choose the correct answer from the options given below.

Options

• Statement I is correct and statement II is incorrect. 

• Statement I is incorrect and statement II is correct. 

• Both statement I and statement II are true. 

• Both statement I and statement II are false.

Answer 1

Both statement I and statement II are true. 

Explanation:

For statement - I

The fastest a cyclist can make a turn on a circular path.

⇒ v ≤ `sqrt(mu"rg") ≤ sqrt(0.2xx2xx9.8)`

⇒ v ≤ `sqrt3.92`

Speed of cyclist, 7 kmh^-1 = `7xx5/18` = 1.94 m/s

The fastest that is safe to travel on a banked frictional road

 `"v"_"allowable"=sqrt("rg"(mu+tantheta)/(1-mutantheta))`

⇒ v = `sqrt((2xx9.8(0.2+tan45°))/(1-0.2xxtan45°))`

= `sqrt((2xx9.8xx1.2)/0.8)`

= 5.42 m/s

Speed of cyclist, 18.5 kmh^-1 = 5.13 m/s

So, both the statements are true.