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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).
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Solution
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 θmax = 1)
sin θmax = 1
⇒ θ = 90°
Matches with option (b)
Hence, tension is least for case (b).
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