A motor cyclist has to rotate in horizontal circles inside the cylindrical wall of inner radius ' R ' metre. If the coefficient of friction between the wall and the tyres is ' _ s ', then the minimum speed required is ( g = acceleration due to gravity)

Step-by-step solution

The minimum speed required for a motorcyclist to ride on a vertical cylindrical wall is derived from equilibrium conditions. The normal force provides centripetal acceleration: N = mv^2 R . Vertical equilibrium requires that friction balances weight: _s N mg . At minimum speed, equality holds: _s N = mg . Substituting the expression for normal force yields _s ( mv^2 R ) = mg . Mass cancels, giving _s v^2 R = g . Solving for velocity: v^2 = Rg _s , so v = Rg _s . The final answer is Rg _s , corresponding to option B