Virtual Work
We will cover following topics
Principle Of Virtual Work
According to the principle of virtual work, the total work done by all the forces acting on a particle is 0 for any virtual displacement.
PYQs
Principle Of Virtual Work
1) Two equal uniform rods \(AB\) and \(AC\), each of length \(l\), are freely jointed at \(A\) and rest on a smooth fixed vertical circle of radius \(r\). If 2\(\theta\) is the angle between the rods, then find the relation between \(l\), \(r\) and \(\theta\), by using the principle of virtual work.
[2014, 10M]
2) A regular pentagon \(\mathrm{ABCDE}\), formed of equal heavy uniform bars jointed together, is suspended from the joint \(\mathrm{A}\), and is maintained in form by a light rod joining the middle points of \(\mathrm{BC}\) and \(DE\). Find the stress in this rod.
[2014, 20M]
3) A solid hemisphere is supported by a string fixed to a point on its rim and to a point on a smooth vertical wall with which the curved surface of the hemisphere is in contact. If \(\theta\) and \(\phi\) are the inclinations of the string and the plane base of the hemisphere to the vertical, prove by using the principle of virtual work that tan \(\phi=\dfrac{3}{8}+\tan \theta\).
[2010, 20M]
4) The middle points of opposite sides of a jointed quadrilateral are connected by light rods of lengths \(l\), \(l'\). If \(T\), \(T'\) be the tensions in these rods, prove that:
\[\dfrac{T}{l}+\dfrac{T'}{l'}=0\][2006, 12M]
5) Two equal uniform rods \(AB\) and \(AC\) of the length \(a\) each, are freely joined at \(A\), and are placed symmetrically over two smooth pegs on the same horizontal level at a distance \(c\) apart \((3 c < 2 a )\). A weight equal to that of a rod, is suspended from the joint \(A\) in the position of equilibrium. Find the inclination of either rod with the horizontal by the principal of virtual work.
[2005, 15M]
6) Five weightless rods of equal lengths are jointed together so as to form a rhombus \(ABCD\) with a diagonal \(BD\). If a weight \(W\) be attached to \(C\) and the system be suspended from a point \(A\), show that the thrust in \(BD\) is equal to \(W/ \sqrt{3}\).
[2002, 15M]
7) The middle points of the opposite sides of a jointed quadrilateral are connected by light rods of lengths, \(l, l^{\prime}\). If \(T\), \(T^{\prime}\) be the tensions in these rods, prove that \(\dfrac{T}{l}+\dfrac{T^{\prime}}{l^{\prime}}=0\).
[2001, 12M]