Three particles A, B and C, each of mass m, form a rigid equilateral triangle of side ℓ hinged at A on a smooth horizontal table. The body rotates about A with angular speed ω. When BC is parallel to the x-axis, a force F is applied at B along BC. Which option gives the correct complete set: (i) hinge-force magnitude before F is applied, and immediately after applying F (ii) x-component and (iii) y-component of the hinge force?

Question

G1 Physics · Accepted Answer

Before F is applied, the rotating triangular body has centripetal acceleration of its centre of mass, giving hinge-force magnitude √3mℓω². Immediately after applying F along BC, use ΣF = M a of CM and Στ about A = Iₐα. Resolving components gives x-component of hinge force = -F/4 and y-component = √3mℓω². Hence option C.