A rod of mass m, length l is hinged at a distance x from the top.A force F is apllied at the bottom.Find x such that hinge reaction is 0.
11basically any hinge reaction has 2 components Fradial anf Ftangential WHEN WE SAY THAT THE HINGE REACTION IS ZERO WE MEAN THAT THE COM IS DOING A VIRCULAR MOTION ABOUT HINGE POINT.
Now the radial component is mw2x while the tangential component is @r (@ mens alpha) .NOW BOTH THE COMPONENTS ARE ZERO.
SO YOU CAN SIMPLY WRITE THE TORQUE EQUATION ABOUT HINGE POINT SUCH THAT T=0 .
I think this way you can find x .
1it is k2/y where k is the radius of gyration of the rod about the the fixed axis and 'y' is the distance of centre of mass of rod from the axis.you can get it by simply conserving leniar momentum of rod as the only external force, reaction force is absent in horizontal direction
1its easy
\Gamma =I_{com}\alpha
or
\Gamma =I_{axis of rotation}\alpha
therefore first calculating it abt the hinge the torque isF(l-x)
and inertiaa abt axis of rotation is....ml^{2}/12+m(L/2-x)^{2}
and torque abt com is....
(F-F_{hinge})l/2=\alpha ml^{2}/12
solving it we get the asner.....
