First slide

Mechanical equilibrium force cases

Question

A chain of mass m is attached at points A and B of a ceiling. Due to its own weight, a sag is there as shown. Then tension at lowest point C is

Moderate

A

$\frac{mg}{2 sinθ}$
B

$\frac{1}{2} mg \cot θ$
C

$\frac{mg}{2}$
D

$\frac{1}{2} mg \tan θ$

Solution

$Weight of segment AC = \frac{mg}{2}$
$∴ For vertical equilibrium, Tsinθ = \frac{mg}{2} - - - - (1) For horizontal equilibrium, Tcosθ = T_{o} - - - - (2) ∴ \frac{T_{o}}{\frac{mg}{2}} = cotθ \Rightarrow T_{o} = \frac{mg}{2} cotθ$

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