PYQs

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 2θ is the angle between the rods, then find the relation between l, r and θ, by using the principle of virtual work.

[2014, 10M]

2) A regular pentagon ABCDE, formed of equal heavy uniform bars jointed together, is suspended from the joint A, and is maintained in form by a light rod joining the middle points of 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 θ and ϕ 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 ϕ=38+tanθ.

[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:

[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 (3c<2a). 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/√3.

[2002, 15M]

7) The middle points of the 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 Tl+T′l′=0.

[2001, 12M]