A block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined an at an angle $\theta$ to the vertical. The minimum value of coefficient of friction between the block and the surface for which the block will remain in equilibrium is :
$\frac{P \cos \theta+Q}{m g-Q \sin \theta}$
$\frac{P+Q \sin \theta}{m g+Q \cos \theta}$
$\frac{P+Q \cos \theta}{m g+Q \sin \theta}$
$\frac{P \sin \theta-Q}{m g-Q \cos \theta}$
Three identical particles are joined together by a thread as shown in the figure. All the three particles are moving on a smooth horizontal plane about point $O$. If the speed of the outer most particle is $v_0$ then the ratio of tension in the three sections of the thread is
A block of mass $m$, is kept on a wedge of mass $M$, as shown in figure such that mass $m$ remains stationary w.r.t. wedge. The magnitude of force $P$ is
A weight can be hung in any of the following four ways by string of same type. In which case is the string most likely to break?
A child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u$ , the centre of mass of the system (trolley + child) will move with a speed