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

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.