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 force acts on a block as shown in figure. Find time when block loses contact with surface.

A coin placed on a rotating table just slips when it is placed at a distance of $1\,cm$ from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of from the centre $............\,cm$

Impending relative motion is opposed by which type of friction ?

The limiting friction between two bodies in contact is independent of

A $2\,kg$ block slides on a horizontal floor with a speed of $4\, m/s$. It strikes a  uncompressed spring, and compresses it till the block is motionless. The kinetic friction  force is $110\,N$ and spring constant is $1000\, N/m$. The spring compresses by ........ $cm$