A recantangular 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:

Options

A. The same in all cases
B. Least in (A)
C. Least in (B)
D. Least in (C)

Answer

C

Explanation

Consider the FBD diagram of the rectangular frame

Balancing vertical forces `2T sin theta- mg= 0` [T is tension in the string]
`rArr 2T sin theta= mg`
Total horizontal force `= T cos theta- T cos theta = 0` Now from Eq. (i) `T= (mg)/(2 sin theta)`
As mg is constant
`rArr T prop (1)/(sin theta) rArr T_("max") = (mg)/(2 sin theta_("min"))`
`sin theta_("min") = 0 rArr theta_("min")= 0`
No option matches with `theta= 0^(@)`
`T_("min")= (mg)/(2 sin theta_("max"))("since", sin theta_("max")=1)`
`sin theta_("max")=1 rArr theta= 90^(@)`
Matches with option (b) Hence tension is least for the case (B). Note : We should be careful when measuring the angle, it must be in the direction as given in the diagram.