Question

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:

A. the same in all cases
B. least in (a)
C. least in (b)
D. least in (c )

Answer 1

Correct Answer - C
Consider the FBD diagram of the rectangular frame

Balancing vertical forces `2T sin theta - mg = 0" [T is tension in the string]"`
`implies " "2T sin theta = mg " .....(i)"`
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 T _("max")=(mg)/(2 sin theta_(min))`
`" "sin theta_("min")=0 implies theta_("min")=0`
No option matches with `theta = 0^(@)`
`T_("min")=(mg)/(2sin theta_("max"))" "("Since, "sintheta_("max")=1)`
`sin theta_("max")=1implies 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.