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?
$\frac {4}{3}\,m$ from steel wire
$\frac {4}{3}\,m$ from brass wire
$1\,m$ from steel wire
$\frac {1}{4}\,m$ from brass wire
Two uniform rods of equal length but different masses are rigidly joined to form an $L-$ shaped body, which is then pivoted as shown in figure. If in equilibrium the body is in the shown configuration, ratio $M/m$ will be
A non-uniform bar of weight $W$ is suspended at rest by two strings of negligible weight as shown in Figure. The angles made by the strings with the vertical are $36.9^{\circ}$ and $53.1^{\circ}$ respectively. The bar is $2\; m$ long. Calculate the distance $d$ of the centre of gravity of the bar from its left end.
$A$ right triangular plate $ABC$ of mass $m$ is free to rotate in the vertical plane about a fixed horizontal axis through $A$. It is supported by a string such that the side $AB$ is horizontal. The reaction at the support $A$ is:
Find minimum height of obstacle so that the sphere can stay in equilibrium.
A metre stick is balanced on a knife edge at its centre. When two coins, each of mass $5\; g$ are put one on top of the other at the $12.0 \;cm$ mark, the stick is found to be balanced at $45.0\; cm$. What is the mass of the metre stick?