As shown in the figure, a block of mass $\sqrt{3}\, kg$ is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3 \sqrt{3}}$. The critical force to be applied on the vertical surface as shown at an angle $60^{\circ}$ with horizontal such that it does not move, will be $3 x$. The value of $3x$ will be

$\left[ g =10 m / s ^{2} ; \sin 60^{\circ}=\frac{\sqrt{3}}{2} ; \cos 60^{\circ}=\frac{1}{2}\right]$

A uniform chain of $6\, m$ length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is $0.5$, the maximum length of the chain hanging from the table is…….$m.$

Meena applies the front brakes, while riding on her bicycle along a flat road. The force that slows her bicycle is provided by the

A heavy body of mass $25\, kg$ is to be dragged along a horizontal plane $\left( {\mu  = \frac{1}{{\sqrt 3 }}} \right).$ The least force required is …….. $kgf$ 

Which of the following is self adjusting in nature?