Question

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;

(a)
(b)
(c)

The tension in the strings will be ______.

Options

• the same in all cases.

• least in (a).

• least in (b).

• least in (c).

Answer 1

The tension in the strings will be least in (b).

Explanation:

Consider the FBD diagram of the rectangular frame

Balancing vertical forces 2T sin θ – mg = 0  ......[T is tension in the string]

⇒ 2T sin θ = mg  ......(i)

Total horizontal force = T cos θ – T cos θ = 0

Now from equation (i), T = `(mg)/(2 sin θ)`

As mg is constant

⇒ `T ∝ 1/sin θ`

⇒ `T_(max) = (mg)/(2 sin θ_(min))`

`sin θ_(min)` = 0

⇒ `θ_(min)` = 0

No option matches with θ = 0°

`T_(min) = (mg)/(2 sin θ_(max))`  ......(since, sin θ_max = 1)

sin θ_max = 1

⇒ θ = 90°

Matches with option (b)

Hence, tension is least for case (b).