$A$ block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\theta$ to the vertical. The block will remain in equilibrium,if the coefficient of friction between it and the surface is

If the mass of block $A = 10\,kg$,the coefficient of static friction $\mu_s = 0.2$,and the coefficient of kinetic friction $\mu_k = 0.2$,find the mass of block $B$ required to start the motion.

The coefficient of friction $\mu$ and the angle of friction $\lambda$ are related as

As shown in the figure,a block of mass $\sqrt{3} \text{ kg}$ is kept on a horizontal rough surface with a coefficient of friction $\mu = \frac{1}{3 \sqrt{3}}$. $A$ force $F$ is applied on the vertical face of the block at an angle of $60^{\circ}$ with the horizontal. The minimum force $F$ required to just move the block is $3x$. Find the value of $3x$.
$\left[ g = 10 \text{ m/s}^2; \sin 60^{\circ} = \frac{\sqrt{3}}{2}; \cos 60^{\circ} = \frac{1}{2} \right]$

The coefficient of static friction between a wooden block of mass $0.5\, kg$ and a vertical rough wall is $0.2$. The magnitude of the horizontal force that should be applied on the block to keep it adhered to the wall will be $N$ $\left[ g = 10\, m/s^2 \right]$.

$A$ 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 ........ $kgf$.