$A$ 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 $g$)

$A$ right triangular plate $ABC$ of mass $m$ is free to rotate in the vertical plane about a fixed horizontal axis through $A$. It is supported by a string at $B$ such that the side $AB$ is horizontal. The reaction at the support $A$ is:

For a system to be in equilibrium,the torques acting on it must balance. This is true only if the torques are taken about

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 $g=10\,m/s^2$)

$A$ physical balance has its arms of unequal length. $A$ body weighs $18 \,kg$ if kept in one pan and weighs $8 \,kg$ if kept in the other pan. The true weight of the body is ............. $kg$

$A$ $3\; m$ long ladder weighing $20\; kg$ leans on a frictionless wall. Its feet rest on the floor $1\; m$ from the wall as shown in the figure. Find the reaction forces of the wall and the floor.