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)
$\sqrt {\cos \alpha } $
$\cos \alpha $
$\sin \alpha $
$\sqrt {\sin \alpha } $
A smooth rod of length $l$ is kept inside a trolley at an angle $\theta$ as shown in the figure. What should be the acceleration a of the trolley so that the rod remains in equilibrium with respect to it?
A uniform rod $AB$ of weight $100\, N$ rests on a rough peg at $C$ and $a$ force $F$ acts at $A$ as shown in figure. If $BC = CM$ and tana $= 4/3$. The minimum coefficient of friction at $C$ is
A uniform meter scale is supported from its $20\ cm$ mark. A body suspended from $10\ cm$ mark keeps the scale horizontal. However, the scale gets unbalanced if the body is completely immersed in water. To regain the balance the body is shifted to the $8\ cm$ mark. Therefore, the specific gravity of the material of the body is
A uniform rod $AB$ is suspended from a point $X$, at a variable distance from $x$ from $A$, as shown. To make the rod horizontal, a mass $m$ is suspended from its end $A$. A set of $(m, x)$ values is recorded. The appropriate variable that give a straight line, when plotted, are
$A$ horizontal force $F = mg/3$ is applied on the upper surface of a uniform cube of mass $‘m’$ and side $‘a’$ which is resting on a rough horizontal surface having $\mu_S = 1/2$. The distance between lines of action of $‘mg’$ and normal reaction $‘N’$ is :