In figure shown, if the magnitude of acceleration of $m,$ is $2\sqrt{N} \mathrm{m} {\mathrm{s}}^{-2},$ given that the string is inextensible and the acceleration of $M$ is $2 \mathrm{m} {\mathrm{s}}^{-2}$ towards left, then find $N$

If hanging block is in equilibrium, then elongation in the spring in c.m. is equal to

In figure shown, pulleys are ideal. Initially the system is in equilibrium and string connecting $m_2$ to rigid support below is cut. What is the initial acceleration (in $\mathrm{m} {\mathrm{s}}^{-2}$) of  $m_2$? (Given $m_1=9 \mathrm{kg}; m_2=3 \mathrm{kg})$

In the arrangement shown in figure, the string and pulley are light. The car starts moving on the horizontal road with constant velocity $5 \mathrm{m} {\mathrm{s}}^{-1}$ towards left. Speed of $2 \mathrm{kg}$ block in $\mathrm{m} {\mathrm{s}}^{-1}$ when $\theta =60°$is

In the arrangement shown in figure the string and pulley are light. Value of$F$ (in $\mathrm{N}$ ) for which $4 \mathrm{kg}$ block will move with $1 \mathrm{m} {\mathrm{s}}^{-2}$ acceleration in the upward direction is

The frictional force (in $\mathrm{N}$) acting between block and the incline is [Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ ]

A force of $10 \mathrm{N}$ is applied on the lower block of mass $5 \mathrm{kg}.$ Acceleration of $5 \mathrm{kg}$ block in $\mathrm{m} {\mathrm{s}}^{-2}$ is $[\mu =0.1]$

A system of $3$ blocks is shown in figure with masses and coefficients of friction indicated in the diagram. What value of maximum horizontal force $F$ can be applied to block $B,$ so that all the three blocks have the same acceleration?