If torque is calculated relative to a reference point and this point is displaced,does the condition for rotation remain valid?

$A$ small ball of mass $m$ is suspended from the ceiling by a string of length $L$. The ball moves along a horizontal circle with constant angular velocity $\omega$, as shown in the figure. The torque about the centre $(O)$ of the horizontal circle is

$A$ uniform metal plate shaped like a triangle $ABC$ has a mass of $540 \,g$. The lengths of the sides $AB, BC$,and $CA$ are $3 \,cm, 5 \,cm$,and $4 \,cm$,respectively. The plate is pivoted freely about the point $A$. What mass must be added to a vertex so that the plate can hang with the long edge $(BC)$ horizontal?

If a street light of mass $M$ is suspended from the end of a uniform rod of length $L$ in different possible patterns as shown in the figure,then

$A$ rod of weight $W$ is supported by two parallel knife edges $A$ and $B$ and is in equilibrium in a horizontal position. The knives are at a distance $d$ from each other. The centre of mass of the rod is at distance $x$ from $A.$ The normal reaction on $A$ is

Two persons of equal height are carrying a long uniform wooden beam of length $\ell$. They are at a distance of $\frac{\ell}{5}$ and $\frac{\ell}{3}$ from the nearest ends of the rod. The ratio of the normal reaction at their heads is