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

One end of a horizontal uniform beam of weight $W$ and length $L$ is hinged on a vertical wall at point $O$ and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point $Q$, at a height $L$ above the hinge at point $O$. A block of weight $\alpha W$ is attached at the point $P$ of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of $(2 \sqrt{2}) W$. Which of the following statement($s$) is(are) correct ?

$(A)$ The vertical component of reaction force at $O$ does not depend on $\alpha$

$(B)$ The horizontal component of reaction force at $O$ is equal to $W$ for $\alpha=0.5$

$(C)$ The tension in the rope is $2 W$ for $\alpha=0.5$

$(D)$ The rope breaks if $\alpha>1.5$

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

A rod of mass $1\ kg$ , length $1\ m$ is suspended horizontally with the help of two ideal strings as shown in figure. First a mass is suspended to the left most end keeping rod horizontal, than a second mass is suspended to the right most end again keeping horizontal orientation. The maximum total mass that can be suspended in that way keeping horizontal orientation of rod ……. $kg.$

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