An object of mass $\sqrt 3$ kg is hung by a string of length $1$ m from the ceiling. Then is object is displaced by $0.5$ m with the help of a horizontal force and kept in equilibrium. Find the tension on the string.
It’s obvious that the $x$ component of the string is $10\sqrt 3$ N, but I am not able to find the $y$ component. The angle of the string can be found in terms of $\tan x=2$ which isn’t very useful. How should I proceed?
Edit: I though o could use the Lami’s theorem to find the answer. Accordingly, $\sin x=\frac{\sqrt 5}{2}$ which is not the right answer. What should I do now?
Therefore the equation should be $$\frac{T}{\sin 90^{\circ}}=\frac{10\sqrt 3}{\sin(180^{\circ}-x)}$$ So $$T=\frac{20\sqrt 3}{\sqrt 5}.$$
Hint.
See the attached forces diagram. Here the black force represents the weight, the blue force is the horizontal reactive force and in red the tension force. At vertex A the angle is $\theta = \arcsin\frac 12$