$A$ 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:

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

Two uniform rods of equal length but different masses are rigidly joined to form an $L-$ shaped body,which is then pivoted as shown in the figure. If in equilibrium the body is in the shown configuration,the ratio $M/m$ will be

Two men are carrying a uniform bar of length $L$ on their shoulders. The bar is held horizontally such that the younger man gets $(1/4)^{th}$ of the load. Suppose the younger man is at the end of the bar,what is the distance of the other man from that end?

$A$ uniform rod of length $200 \, cm$ and mass $500 \, g$ is balanced on a wedge placed at $40 \, cm$ mark. $A$ mass of $2 \, kg$ is suspended from the rod at $20 \, cm$ and another unknown mass $'m'$ is suspended from the rod at $160 \, cm$ mark as shown in the figure. Find the value of $'m'$ such that the rod is in equilibrium. $(g = 10 \, m/s^2)$

Find the value of $T_1$ (in $N$),if the system is in equilibrium and the mass of the rod is $10 \ kg$ and its length is $10 \ m$. $[g = 10 \ m/s^2]$ (in $N$)