Vehicle turning on a circular path: Dependence of the banking/lean angle on mass. Context: A vehicle moves along a horizontal circular path of radius R at speed v (steady turn). Choose the correct statement regarding how the angle of inclination depends on vehicle mass.

Given data

• Vehicle negotiates a curve of radius R at speed v.

Concept/Approach
For a vehicle that leans (or a banked road), the required lean/bank angle θ satisfies tanθ = v² / (gR) which does not include the vehicle mass m.

Step-by-step reasoning
Centripetal requirement: Resultant of weight and normal provides v²/R. From force balance, tanθ = (centripetal acceleration)/g = v²/(gR). No mass term appears ⇒ θ is independent of mass.

Common pitfall
Confusing tyre–road friction limits (which depend on normal reaction) with the geometric relation for the required angle, which is mass-independent.

Final Answer
Independent of mass