D: t = mgx? Lsinθ
Let the magnitude of the force exerted by the hinge on the plate be F, and decompose F into horizontal right component Fx and vertical upward component Fy, which are obtained from the equilibrium conditions: Fx=Tcosθ,
Tsinθ+Fy=mg
Simultaneous solution: Fx=mgcotθ? xL,Fy=mg( 1-xL)
Let xL=y
F=F2X+F2y=mgcotθ2y2+( 1? y)2=mg(cotθ2+ 1)y2? 2y+ 1
According to mathematical knowledge, f first decreases and then increases.
So choose d