This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the forces acting on the person. For the person to remain stuck to the wall, the upward static frictional force (f_s) must balance the downward gravitational force (weight, Mg). f_s Mg The normal force (N) exerted by the wall on the person provides the centripetal force required for circular motion. N = M^2 r where M is the mass, is the angular velocity, and r is the radius of the drum. Step 2: Apply the condition for static friction. The maximum static frictional force is given by f_s,max = N, where is the coefficient of static friction. For the person not to slide down, the frictional force must be at least equal to the weight: N Mg Step 3: Substitute the expression for the normal force into the friction inequality. Substitute N = M^2 r into the inequality: (M^2 r) Mg Step 4: Solve for the minimum angular velocity (_min). To find the minimum angular velocity, we set the inequality to an equality: M_min^2 r = Mg Divide both sides by M: _min^2 r = g Solve for _min^2: _min^2 = (g)/( r) Take the square root of both sides: _min = sqrt((g)/( r)) Comparing this with the given options, option (a) matches our result. The final answer is (a) \ _min = sqrt((g)/( r)). Send me the next one 📸