Concepts Of Physics MCQ Edition [Volume 1]PhysicsCircular Motion
A car of mass m attempts to navigate a circular road of radius r which is banked for a speed v = 40 km/hr . The coefficient of friction between the tyre and the road is negligible.
Options
- AIf the car attempts the turn at a speed lower than 40 km/hr , it will slip downwards
- BThe car is unable to execute a turn without skidding
- CWhen the car turns at the exact speed of 40 km/hr , the force exerted by the road on the car exceeds mg and al
- DWhen the car turns at the exact speed of 40 km/hr , the force exerted by the road on the car equals mv^2 r
Correct answer
C. When the car turns at the exact speed of 40 km/hr , the force exerted by the road on the car exceeds mg and al
Step-by-step solution
The road is banked at an angle such that = v₀^2 rg , where v₀ = 40 km/hr . When the car moves at a speed v , the forces acting on it are the normal force N and gravity mg . Resolving forces along the incline, the downward component of gravity is mg and the required centripetal component is mv^2 r . If v mv^2 r . Since friction is negligible, there is a net downward force along the incline, causing the car to slip downwards. Thus, option (1) is correct. When the car moves at exactly v = 40 km/hr , it does not slip.