Question

A uniform rod has mass m and length L. One end of the rod is attached to a fixed point O by a hinge at the top of a wall and an additional force F is applied to the other end of the rod in the horizontal direction shown. Given that the rod is in mechanical equilibrium, what is the magnitude of the applied force F, expressed as a numerical multiple of mg, where g is the magnitude of the acceleration due to gravity? Express your answer by entering a decimal number, specified to 3 significant figures,

Answer 1

find net torque due to both the forces at point O.Then find F on equating them

o g Answer! If system is in equilibrium at point o Hence net torque is zeuo at point o. ex- Too que due to mg B . F (OA) ng = t sinsong og = 0.2 singl (Cluckurise) ning 2= Torque due to f t2 = @B) XF= (d Cos 30 ) = for = 0.866 LF anticlockwise renet = -21 = = -2, 272 = 0.866 LF = 0.25ing a - 0.866 = mg 0.25 F and fa 0.25 mg 0.866 o (F= 0.288 mg