Question

A circular road of radius r is banked for a speed of v = 40km/h. A car of mass m attempts to go on the circular road. The friction coefficient between the tyre and the road is negligible. Then- 

(A) The car cannot make a turn without skidding 

(B) If the car turn at a speed less than 40km/h, it will slip down. 

(C) If the car turns at the correct speed of 40km/h the force by the road on the car is equal to mv² /r 

(D) If the car turns at the correct speed of 40 km/h, the force by the road on the car is greater that mg as well as greater than mv² /r

Answer 1

Correct options are (B) and (D)

Since µ ≈ 0, there would be no frictional force.

N cosθ = mg

Now when speed of the car is less than v_c = 40 km/hr and if we consider the frame of car;

Both these forces are made equal through proper banking.

⇒ It slips downwards.

Answer 2

Correct answer is 

(B) If the car turn at a speed less than 40km/h, it will slip down. 

(D) If the car turns at the correct speed of 40 km/h, the force by the road on the car is greater that mg as well as greater than mv²/r