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

(c) Consider the FBD diagram of the rectangular frame

Balancing vertical force `2T "sin"theta-mg=0" "`[T is tension in the string]
`implies " "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
`implies T prop (1)/("sin"theta)`
`implies "sin"theta_("min")=0impliestheta_("max")=0`
No option matches with `theta=0^(@)`
`T_("min")=(mg)/(2"sin"theta_("max"))" "("since " "sin"theta_("max")=1)`
`"sin"theta_("max")=1impliestheta=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.