$A$ man can move on a horizontal plank supported symmetrically as shown. The variation of normal reaction on support $A$ with distance $x$ of the man from the end of the plank is best represented by :

Consider the situation shown in the figure. Uniform rod of length $L$ can rotate freely about the hinge $A$ in vertical plane. Pulleys and string are light and frictionless. If therod remains horizontal at rest when the system is released then the mass of the rod is :

A thin rod $MN$, free to rotate in the vertical plane about the fixed end $N$, is held horizontal . When the end $M$ is released the speed of this end, when the rod makes an angle $\alpha $ with the horizontal, will be proportional to ( see figure)

$A\, 5\, m$ long pole of $3\, kg$ mass is placed against a smooth vertical well as shown in the figure. Under equilibrium condition, if the pole makes an angle of $37^o$ with the horizontal, the frictional force between the pole and horizontal surface is

Two particles of mass $m$ each are fixed at the opposite ends of a massless rod of length $5m$ which is oriented vertically on a smooth horizontal surface and released. Find the displacement of the lower mass on the ground when the rod makes an angle of $37^o$ with the vertical. ........ $m$

A uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A.$ The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $ml^2/3$, the initial angular acceleration of the rod will be