Question

A body moves along an uneven horizontal road surface with constant speed at all points. The normal reaction of the road on the body is 

(a) maximum at A 

(b) maximum at B 

(c) minimum at C 

(d) the same at A, B and C

Answer 1

Correct Answer is: (a) maximum at A

Let r_A, r_B and r_C be the radii of curvature of the road surface at A, B and C respectively. Let N_A, N_B and N_C be the normal reactions of the road on the body at A, B and C respectively. The centres of curvature of the road surface lie above the road at A and C, and below the road at B.

∴ N_A - mg = mv ²/r_A, mg - N_B = mv ²/r_B, N_C - mg = mv ₂/r_C.

Clearly, N_A and N_C are > N_B. Also, as r_A < r_C, from the figure, 

N_A = mg + mv² / r_A > N_C = mg + mv² / r_C .