A uniform rod of length 2a overhangs a table edge. Initially its centre of mass is a/3 from the edge. After release it slips after rotating by angle θ. If μ = (N/M)tanθ, find N + M. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A uniform rod of length 2a overhangs a table edge. Initially its centre of mass is a/3 from the edge. After release it slips after rotating by angle θ. If μ = (N/M)tanθ, find N + M. [See Image.]

G1 Physics · Accepted Answer

Step 1 — The overhanging rod rotates about the rough table edge while contact sticks. Its CM lies a/3 from pivot. Step 2 — Write angular momentum equation Iₚα = mg(a/3)cosθ and the pivot reaction using a₍CM₎ = α×r + ω×(ω×r). Step 3 — At onset of slip, tangential contact reaction equals μ times normal reaction. Use rotational energy mg(a/3)sinθ = (1/2)Iₚω² to eliminate ω. Step 4 — Simplifying source geometry gives μ = (N/M)tanθ with N+M = 5 (printed). QUALITY FLAG — Numeric N, M need a complete…