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)

$A$ body is in equilibrium under the influence of a number of forces. Each force has a different line of action. The minimum number of forces required is

A non uniform cylinder of mass $m$ , length $l$ and radius $r$ is having its cetnre of mass at a distance $l/4$ from the centre and lying on the axis of the cylinder. The cylinder is kept in a liquid of uniform density $\rho $ . The moment of inertia of the rod about the centre of mass is $I$ . The angular acceleration of point $A$ relative to point $B$ just after the rod is released from the position shown in figure is

$A\, 5\, m$ 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

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 figure. It is supported by a cable $A B$ such that the system is in equilibrium. The tension in the cable is $…………\,N$ (Take $g=10\,m / s ^2$ )