$A$ false balance has unequal arms. An object weighs $X$ when placed in one pan and $Y$ when placed in the other pan. The true weight $W$ of the object is equal to:

An object of mass $8\,kg$ is hanging from one end of a uniform rod $CD$ of mass $2\,kg$ and length $1\,m$ pivoted at its end $C$ on a vertical wall as shown in the figure. It is supported by a cable $AB$ such that the system is in equilibrium. The tension in the cable is $............\,N$ (Take $g=10\,m/s^2$)

$A$ uniform rod of mass $250 \ g$ having length $100 \ cm$ is balanced on a sharp edge at $40 \ cm$ mark. $A$ mass of $400 \ g$ is suspended at $10 \ cm$ mark. To maintain the balance of the rod,the mass to be suspended at $90 \ cm$ mark is: (in $g$)

$A$ metal rod of weight $W$ is supported by two parallel knife-edges $A$ and $B$. The rod is in equilibrium in a horizontal position. The distance between the two knife-edges is $r$. The centre of mass of the rod is at a distance $x$ from $A$. The normal reaction on $A$ is

$A$ car weighs $1800 \; kg$. The distance between its front and back axles is $1.8 \; m$. Its centre of gravity is $1.05 \; m$ behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.

Write the condition for rotational equilibrium and translational equilibrium.