A uniform rod of mass m and length l which can rotate freely in vertical plane without friction, is hinged at its lower end on a table. If a sphere of mass m and radius R=L3 is placed in contact with the vertical rod and a horizontal force F = 80 N is applied at the upper end of the rod. Find the horizontal component of hinge reaction (in N) acting on the rod just after force F starts acting.

Torque equation for rod about O, I0α=Fl−Nl3∴ ml23⋅α=Fl−Nl3mlα3=F−N3             …(i)The motion of the sphere is translational only acceleration of the sphere (a) = acceleration of point Plα3=a                        …(ii)From (i) and (ii) ma=F−N3            …(iii)For sphere, N=ma                          …(iv)Solving (iii) and (iv) we get, a=3F4m∴N=3F4Acceleration of the COM of the rod isacm=αl2=3a2=9F8mLet horizontal component of hinge reaction is Nx. Force equation for rod, F−3F4+Fx=mac⇒F−3F4+Fx=m9F8mFx=9F8−F4=7F8=7×808=70 N