A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports as shown in figure. It can be done in one of the following three ways, The tension in the strings will be

Options

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

Answer

C

Explanation

We get the FBD of rectangular frame in the figure.

If T is the tension in the string, so vertical and horizontal components of it are as shown in figure.
For balancing vertical forces,
` 2 T sin theta - mg =0`
`therefore 2T sin theta = mg therefore T = (mg )/(2 sin theta) " "...(1)`
For balancing horizontal forces,
`T cos theta - T cos theta =0`
In equation (1) mg is same.
`therefore T prop (1)/( sin theta)`
`If theta _(min) implies T max`
but ` theta_(min) = 0^(@)`
`therefore T_(max) prop (1)/( sin theta)`
`therefore T _(max)` is infinite but `theta =0.6 ^(@)`is not given.
If `theta_(max) implies T _(min)`
`therefore But theta _(max) = 90^(@)` hence `T _(min) prop (1)/( sin 90^(@))`
`therefore T_(min) prop 1` which is least tension.