Three blocks of masses $4\, kg, 8\, kg$ and $24\, kg$ are connected to each other with light strings and placed on a smooth horizontal floor as shown in the figure. If the system moves with an acceleration of $2\, m/s^2$,the applied force $F$ is ............ $N$.

Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface. The acceleration of mass $m$ is:

$A$ trolley of mass $20 \ kg$ is attached to a block of mass $4 \ kg$ by a massless string passing over a frictionless pulley as shown in the figure. If the coefficient of kinetic friction between the trolley and the surface is $0.02$,then the acceleration of the trolley and block system is (take $g=10 \ ms^{-2}$):- (in $ms^{-2}$)

$A$ car of mass $1000\,kg$ is moving at a speed of $30\,m/s.$ Brakes are applied to bring the car to rest. If the net retarding force is $5000\,N,$ the car comes to stop after travelling $d\,m$ in $t\,s.$ Then

$A$ block of mass $m$ slides on a wooden wedge,which in turn slides backward on a horizontal surface. The acceleration of the block with respect to the wedge is: Given $m = 8 \, kg, M = 16 \, kg$. Assume all surfaces shown in the figure to be frictionless.

$A$ uniform rope of mass $1.0\, kg$ is connected to a box of mass $2.0\, kg$,which is placed on a smooth horizontal surface. The free end of the rope is pulled horizontally by a force of $6\, N$. Find the tension at the midpoint of the rope in $N$.