Two blocks are connected by a spring. The combination is suspended, at rest, from a string attatched to the ceiling, as shown in the figure. The string breaks suddenly. Immediately after the string breaks, what is the initial downward acceleration of the upper block of mass $2\,m$ ?

A block placed on a rough inclined plane of inclination $\left(\theta=30^{\circ}\right)$ can just be pushed upwards by applying a force " $F$ " as shown. If the angle of inclination of the inclined plane is increased to $\left(\theta=60^{\circ}\right)$, the same block can just be prevented from sliding down by application of a force of same magnitude. The coefficient of friction between the block and the inclined plane is

Two masses of $5\, kg$ and $10\, kg$ are connected to a pulley as shown. What will be the acceleration if the pulley is set free ($g =$ acceleration due to gravity)

Two masses $A$ and $B$ of $10\,kg$ and $5\,kg$ respectively are connected with a string passing over a fricionless pulley fixed at the corner of a table as show $n$ in figure. The coefficient of friction of $A$ with the table is $0.2$ . The minimum mass of $C$ that may be placed on $A$ to prevent if from moving is equal to $...........\,kg$

The maximum "$F$" which will not cause motion of any of the blocks $............\,N$

A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m$. If a force $P$ is applied at the free end of the rope, the force exerted by the rope on  the block is-