A uniform rod of mass m and length ℓ is suspended by two vertical inextensible strings. Immediately after cutting one string, tension in the other is mg/n. Determine n. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A uniform rod of mass m and length ℓ is suspended by two vertical inextensible strings. Immediately after cutting one string, tension in the other is mg/n. Determine n. [See Image.]

G1 Physics · Accepted Answer

Step 1 — Immediately after one supporting string breaks, the other end is constrained to have zero acceleration along its remaining vertical string. Step 2 — Write vertical translation equation mg−T = ma₍CM,y₎ and torque about centre I₍CM₎α = (T ℓ)/2. Step 3 — For initial horizontal rod with its free end beginning to rotate downward, kinematic constraint a₍CM,y₎ = αℓ/2. Step 4 — With I₍CM₎ = mℓ²/12, solve the equations and obtain T = mg/4. Step 5 — Hence n = 4.