Resultant force acting vertically downwards on the rod
=P + Q + R + S + T + W
= 1 + 2 + 3 + 4 + 5 + 4 = 19 kg wt
Thus force of 19 kgwt. acting vertically upwards will balance the rod. This force acts at a distance ‘x’ from A.
i.e., R1 = 19 kgwt.
Taking the moments about A,
P × AB + Q × AC + R × AD + S × AE + T × AF + W × Al = R1x.
1 × 1 + 2 × 2 + 3 × 3 + 4 × 4 + 5 × 5 + 4 × 3 = R1x = 19x.
1 + 4 + 9 + 16 + 25 + 12 = 19x.
67 = 19x or x = \(\frac {67}{19}\) = 3.52m
∴ Distance of the knife edge from the end A is 3.52m.