A uniform horizontal beam AB AB\,AB has a length of 6 m and a mass of 10 kg. The beam is supported in a horizontal position of static equilibrium by two vertical light strings. One string is attached at end A A\,A with tension TAT_ATA, and the other is attached at a point CCC, which is a distance d d\,d from end BBB, with tension TCT_CTC. A block of mass 20 kg is placed on the beam at a distance of 1.5 m from AAA, as shown in the diagram.
Given that the tension in the string at A A\,A is 1.5 times the tension in the string at CCC (TA=1.5TCT_A = 1.5 T_CTA=1.5TC), find the value of ddd.
1.0 m1.0\text{ m}1.0 m
2.25 m2.25\text{ m}2.25 m
5.0 m5.0\text{ m}5.0 m
2.67 m2.67\text{ m}2.67 m