Vehicle Dynamics – Overturning on a Level Circular Path\nTo avoid overturning while negotiating a level (unbanked) circular path, the speed of the vehicle must be __________ a certain critical value.

Introduction / Context:
While turning on a level (unbanked) road, a vehicle experiences lateral acceleration requiring a centripetal force. If speed is too high, the lateral load transfer can lead to wheel lift and overturning.

Given Data / Assumptions:

• Level (unbanked) circular path of radius r.
• Vehicle with track width b, center-of-gravity height h, and mass m.
• Static friction provides lateral force; rollover is considered based on tipping about the outer wheels.

Concept / Approach:
Overturning begins when the resultant of weight and inertial (centrifugal) effect passes through the outer tire contact edge. The critical speed v_crit can be estimated from moment balance about the outer wheel contact line.

Step-by-Step Solution:
Centrifugal effect (in vehicle frame) = m v^2 / r acting laterally at height h. Weight W = m g acting downward through CG; half-track b/2 is the lever arm to the outer wheel line. At impending overturn: (m v^2 / r) * h = W * (b/2) = m g * (b/2). Solve: v_crit = sqrt( (g r b) / (2 h) ). To avoid overturning, the operating speed v must be less than v_crit.

Verification / Alternative check:
The same criterion is obtained via resultant force line passing within the base of support. Banking raises the allowable speed; level path is the limiting case here.

Why Other Options Are Wrong:
'Greater than' or 'equal to': at or above the critical speed, overturning risk exists. 'Independent of': speed clearly governs lateral acceleration. 'Randomly varying': physically meaningless.

Common Pitfalls:
Confusing skid (friction limit) with roll-over (geometric + inertial limit). Both impose speed limits but via different criteria.

Final Answer:
less than