A uniform rod of mass m and length ℓ is hinged at its upper end and is given the minimum angular speed needed to complete a vertical circle. Which option correctly gives both (i) the required initial angular speed and (ii) the tension at the centre of the rod at the initial instant?

Question

G1 Physics · Accepted Answer

For the minimum speed needed to complete the circle, energy gives ½(mℓ²/3)ω² = mgℓ, so ω=√(6g/ℓ). At the initial lowest position, the centre of mass has radial acceleration ω²ℓ/2. Force balance along the rod gives T-mg = mω²ℓ/2, hence T=11mg/4. Therefore option C.