A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports (figure). It can be done in one of the following three ways;

The tension in the strings will be:

1. the same in all cases. 2. least in (a).
3. least in (b). 4. least in (c).
(3) Hint: The weight of the frame is balanced by the tension developed in the strings.
Step 1: Find the tension developed in the strings in a general case.
Consider the FBD diagram of the rectangular frame.
Balancing vertical forces, 2T sinθ-mg=0                  [T is the tension in the strings]
                                    2T sinθ= mg                                                        ...(i)
Total horizontal force = T cosθ-T cosθ=0
Now from Eq. (i), T=mg2sinθ
Step 2: Find the minimum tension in the strings.
As mg is constant,
T1sinθ
Tmin=mg2 sinθmax                (since, sinθmax=1)
sinθmax=1θ=90°
Matches with option(b).
Hence, the tension is least for case(b).