If three coplanar concurrent forces acting at a point ‘O’ are in equilibrium then

the ratio of T1 /T2 और T1 /T_{3} respectively will be?

This question was previously asked in

ISRO LPSC Technical Assistant Mechanical held on 04/03/2018

Option 1 : \(\sqrt3\) and \({\frac{\sqrt3}{2}}\)

CT 1: Growth and Development - 1

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10 Questions
10 Marks
10 Mins

__Concept:__

Lami's theorem:

Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear forces, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding forces. According to the theorem:

\(\frac{A}{{\sin \alpha }} = \frac{B}{{\sin\beta }} = \frac{C}{{\sin\gamma }}\)

__Calculation__:

**Given:**

From the given figure we have

\(\frac{T_1}{sin~(120)}~=~\frac{T_2}{sin~(150)}~=~\frac{T_3}{sin~(90)}\)

By solving the above equation we have,

\(\frac{T_1}{T_2}~=~\sqrt3\) and \(\frac{T_1}{T_3}~={\frac{\sqrt{3}}{2}}\)