question_answer 8)

A non-uniform bar of weight W is suspended at rest by two strings of negligible weights as shown in Fig. 7.100. The angles made by the strings with the vertical are 36.9° and 53.1° respectively. The bar is 2 m long. Calculate the distance d of the centre of gravity of the bar from its left end.     Fig. 7.100  

Answer:

Let  and  be the tensions in the two strings, as shown in Fig. 7.101.   Fig. 7.101 For translational equilibrium, on balancing the vertical components of forces, we get                     ?(1) On balancing the horizontal components, we get                                ...(2) For rotational equilibrium, we balance the torques about the CG of the bar. Clockwise torque = Anticlockwise torque                      ?(3) Dividing (3) by (2), we get   or            or            or            or                 or              .