As shown in the figure, a block of mass √ 3 kg is kept on a horizontal rough surface of coefficient of friction 1/(3 √ 3). The critical force to be…

As shown in the figure, a block of mass $\displaystyle \sqrt{3} \mathrm{~kg}$ is kept on a horizontal rough surface of coefficient of friction $\displaystyle \frac{1}{3 \sqrt{3}}$. The critical force to be applied on the vertical surface as shown at an angle $\displaystyle 60^{\circ}$ with horizontal such that it does not move, will be $\displaystyle 3 x$. The value of $\displaystyle x$ will be \_\_\_\_. $\displaystyle \left[\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 ; \sin 60^{\circ}=\frac{\sqrt{3}}{2} ; \cos 60^{\circ}=\frac{1}{2}\right]$