A block of $$\sqrt{3}$$ kg is attached to a string whose other end is attached to the wall. An unknown force $$F$$ is applied so that the string makes an angle of $$30°$$ with the wall. The tension $$T$$ is: (Given $$g = 10$$ m s$$^{-2}$$)

First lets write the Forces acting in Vertical and Horizontal direction

In the Vertical direction,

Forces are $$F_g=\sqrt{\ 3}g\ due\ to\ gravity\ and\ T\ \left(\ tension\ of\ the\ rope\right)$$

and in Horizontal , The forces are $$F\left(appplied\ force\right)\ and\ T\cos\theta\ \left(tension\ of\ the\ rope\right)$$

First lets equate the Vertical Forces 

$$\sqrt{\ 3}g\ =\ T\cos\ \theta\ $$

$$10\sqrt{\ 3}=\ T\times\ \frac{\sqrt{\ 3}}{2}$$

$$\ T=20N$$