$A$ uniform rod of length $L$ and weight $W$ is suspended horizontally by two vertical ropes as shown. The first rope is attached to the left end of the rod while the second rope is attached at a distance $L/4$ from the right end. The tension in the second rope is

$A$ 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:

In an experiment with a beam balance,an unknown mass $m$ is balanced by two known masses of $16\, kg$ and $4\, kg$ as shown in the figure. The value of the unknown mass $m$ is ....... $kg$.

$A$ rod of mass $M = 1 \ kg$ and length $L = 1 \ m$ is suspended horizontally by two ideal strings as shown in the figure. The strings are attached at a distance of $1/3 \ m$ from each end. First, a mass $m_1$ is suspended from the left end while keeping the rod horizontal. Then, a second mass $m_2$ is suspended from the right end, again keeping the rod horizontal. What is the maximum total mass $(m_1 + m_2)$ that can be suspended in this way while maintaining the horizontal orientation of the rod?

$A$ non-uniform bar of weight $W$ is suspended at rest by two strings of negligible weight as shown in the figure. The angles made by the strings with the vertical are $36.9^{\circ}$ and $53.1^{\circ}$ respectively. The bar is $2 \; m$ long. Calculate the distance $d$ of the centre of gravity of the bar from its left end.

$A$ weightless rod is acted on by upward parallel forces of $2N$ and $4N$ at ends $A$ and $B$ respectively. The total length of the rod $AB = 3m$. To keep the rod in equilibrium,a force of $6N$ should act in the following manner: