$A$ thin rod of length $L$ is placed vertically on a frictionless horizontal floor and released with a negligible push to allow it to fall. At any moment, the rod makes an angle $\theta$ with the vertical. If the center of mass has acceleration $= A$, and the rod an angular acceleration $= \alpha$ at initial moment, then
$A= (L\alpha ).sin\theta$
$A/2 = (L\alpha ).sin\theta$
$2A = (L\alpha ).sin\theta$
$A = L\alpha$
A light rod of length $200\,cm$ is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross-section $0.1\,cm^2$ and the other of brass of cross-section $0.2\,cm^2$ . Along the rod at which distance a weight may be hung to produce equal stresses in both the wires?
$ABC$ is an equilateral triangle with $O$ as its centre. $\vec F_1, \vec F_2 $and $\vec F_3$ represent three forces acting along the sides $AB, BC$ and $AC$ respectively. If the total torque about $O$ is zero then the magnitude of $\vec F_3$ is
Two vertical walls are separated by a distance of $2\ m$. Wall $A$ is smooth while wall $B$ is rough with a coefficient of friction $0. 5$. A uniform rod is placed between them as shown. The length of longest rod that can be placed between walls is equal to
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)
Two men are carrying a uniform bar of length $L$, on their shoulders. The bar is held horizontally such that younger man gets $(1/4)^{th}$ load. Suppose the younger man is at the end of the bar, what is the distance of the other man from the end