Question

A beam AB (fig.a) is hinged at A and supported at B by a vertical cord, which passes over two frictionless pulleys C and D. If pulley D carries a vertical load Q, find the position x of the load P if the beam is to remain in equilibrium in the horizontal position.

Answer 1

First consider the free body diagram of block Q, From the fig.(b)

2T = Q, T = Q/2

i.e tension in the rope = Q/2

Now consider the F.B.D. of the beam as shown in fig(c) Here two forces are acting force ‘P’ at a distance ‘X’ from point ‘A’ and T = Q/2 at a distance ‘l’ from point ‘A’ 

Taking moment about point ‘A’, i.e. ∑M_A = 0

P X x = Q/2 X l

X = QL/2p.