In the given arrangement,all surfaces are smooth. What acceleration $a$ should be given to the system (block $M$) so that the block $m_2$ does not slide down?

$A$ thief stole a box full of valuable articles of weight $W$ and while carrying it on his back,he jumped down a wall of height $h$ from the ground. Before he reached the ground,he experienced a load of:

$A$ container of mass $m$ is pulled by a constant force $F$. Inside the container,a second block of the same mass $m$ is placed,connected to the wall by a massless spring of constant $k$. Initially,the spring is at its natural length. Find the velocity of the container at the instant the compression in the spring is maximum for the first time.

$A$ box of mass $m \, kg$ is placed on the rear side of an open truck accelerating at $4 \, m/s^2$. The coefficient of friction between the box and the surface below it is $0.4$. The net acceleration of the box with respect to the truck is zero. The value of $m$ is :- $[g = 10 \, m/s^2]$

Two blocks of masses $2 \,kg$ and $4 \,kg$ are hanging with the help of a massless string passing over an ideal pulley inside an elevator. The elevator is moving upward with an acceleration $\frac{g}{2}$. The tension in the string connected between the blocks will be .......... $N$ (Take $g=10 \,m/s^2$).

$A$ rough vertical board has an acceleration $a$ so that a $2 \ kg$ block pressing against it does not fall. The coefficient of friction between the block and the board should be