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
$\frac{{(P + Q\sin \theta )}}{{(mg + Q\cos \theta )}}$
$\frac{{(P\cos \theta + Q)}}{{(mg - Q\sin \theta )}}$
$\frac{{(P + Q\cos \theta )}}{{(mg + Q\sin \theta )}}$
$\frac{{(P\sin \theta - Q)}}{{(mg - Q\cos \theta )}}$
A block $A$ of mass $m_1$ rests on a horizontal table. A light string connected to it passes over a frictionless pully at the edge of table and from its other end another block $B$ of mass $m_2$ is suspended. The coefficient of kinetic friction between the block and the table is $\mu _k.$ When the block $A$ is sliding on the table, the tension in the string is
A body is pulled along a rough horizontal surface with a velocity $6\,m/s$. If the body comes to rest after travelling $9\,m$ , then coefficient of sliding friction, is- (Take $g = 10\,m/s^2$ )
A block of mass $M = 5\,kg$ is resting on a rough horizontal surface for which the coefficient of friction is $0.2$. When a force $F = 40\,\,N$ is applied, the acceleration of the block will be ........ $m/\sec^2$ $(g = 10\,\,m/{\sec^2})$
Two blocks $A$ and $B$ of masses $5 \,kg$ and $3 \,kg$ respectively rest on a smooth horizontal surface with $B$ over $A$. The coefficient of friction between $A$ and $B$ is $0.5$. The maximum horizontal force (in $kg$ wt.) that can be applied to $A$, so that there will be motion of $A$ and $B$ without relative slipping, is
A block of mass $M$ placed on rough surface of coefficient of friction equal to $3$ . If $F$ is the $(4/5)$ of the minimum force required to just move. Find out the force exerted by ground on the block